Timeless Quanta: A Threshold for Mass, Entropy, and the Arrow of Time

Timeless Quan a: A Th eshold Geome y o Mass, En opy,
and Time
Johnny Rouse1
1Rouse Nexus LLC, G een ille, NC, USA , ORCID: 0009-0002-8095-6258 ,
[email p o ec ed]
Oc obe 2025, Ve sion 3.0 (Rep oducible Release)
Abs ac
This wo k p esen s he Timeless Quan a (TQ) amewo k: a h eshold geome y whe e
mass, en opy, and he di ec ion o ime eme ge om a uni e sal cu a u e condi ion. All
scales a e de i ed om a single dimensional ancho , he collapse adius c, calib a ed o
he p o on mass h ough Koma ene gy equi alence. The cu a u e- h eshold condi ion
de ines one quan um o in eg a ed cu a u e, ixing σ, while Koma no maliza ion de e mines
L. A Bol zmann-weigh ed he mal ac i a ion in eg al yields he ba yon asymme y ac o
(α)=0.061 ±0.008. Collapse occu s when Ricci cu a u e exceeds a c i ical h eshold Θc,
o ming quan ized shells wi h a hyb id Gaussian-exponen ial p o ile. No addi ional empi ical
pa ame e s a e in oduced, yielding p edic ions ac oss pa icle physics and expe imen al
domains. En opy ollows a Bekens ein-Hawking-like law wi h a cu a u e-scale coupling
Gsde i ed a he collapse scale, p oducing ini e shell en opy consis en wi h hea y-ion
da a. The Koma -co ec ed ene gy ep oduces he p o on mass o 0.04% [1]; he Higgs mass
eme ges a 125 GeV [2,3]. The amewo k issued ou speci ic, publicly a chi ed p edic ions
o ALICE Run 3 oxygen–oxygen collisions p io o da a elease [22], p o iding an immedia e
expe imen al es o he cu a u e-collapse hypo hesis.
1 In oduc ion
The S anda d Model o pa icle physics emains incomple e, elying on unexplained cons an s
and phenomena such as he o igin o pa icle masses and he ine-s uc u e cons an α[10]. A
comple e heo y mus explain hese wi hou a bi a y pa ame e s. The Timeless Quan a (TQ)
amewo k p oposes ha a uni e sal cu a u e h eshold Θc—mo i a ed by he need o uni y
mass, en opy, and ime o igins—go e ns he ac i a ion o quan ized collapse shells. When local
Ricci cu a u e su passes Θc, space ime ansi ions om a cohe en , Ricci- la con igu a ion o a
disc e ized shell s uc u e wi h a hyb id Gaussian-exponen ial p o ile, gene a ing mass, en opy,
and empo al o ien a ion di ec ly om geome y.
All pa ame e s a e de i ed om a single geome ic calib a ion— he collapse adius c—which
is ixed by equa ing he Koma ene gy o he shell o he p o on es mass. F om his single
scale, in e nal p o ile pa ame e s (σ,L, e c.) a e ixed by con inui y and s abili y, yielding a
ully de e mined geome y. Wi h no unable pa ame e s beyond he geome ic ancho , he model
de i es:
•P o on mass—calcula ed ia Koma -co ec ed shell ene gy, accu a e o 0.04% [1].
•Higgs mass—de i ed h ough cu a u e-o e lap scaling, consis en wi h 125 GeV [2,3].
•Lep on anomalous momen s— ia cu a u e-spin coupling [4].
1
•Fini e shell en opy—a em ome e scales.
•Hea y-ion en opy p oduc ion—ma ching RHIC/LHC da a [7].
The amewo k de i es ou alsi iable p edic ions o ALICE Run 3 oxygen–oxygen colli-
sions, publicly documen ed on July 1, 2025, es ablishing a di ec es o TQ’s cu a u e-collapse
dynamics [22].
The pape p oceeds as ollows: Sec ion 2 in oduces he collapse geome y and h eshold
condi ion; Sec ion 3 de i es he p o on mass and ancho s he scale; Sec ion 4 de elops en opy
and ime’s di ec ion; Sec ions 5–7 ex end he amewo k o bosonic modes, eno maliza ion, and
empo al o ien a ion; Sec ion 8 summa izes uni ied p edic ions and es s; Sec ion 9 discusses
scope and alsi iabili y. De ailed de i a ions a e in Appendix A.
2 Collapse Geome y and Th eshold Condi ion
This sec ion o malizes he h eshold-collapse geome y unde pinning he TQ amewo k. Space-
ime cu a u e is supp essed du ing quan um cohe ence and eins a ed when he collapse condi-
ion is igge ed. The go e ning pos ula e is ha a uni e sal cu a u e h eshold Θcde e mines
when he cohe en s a e ansi ions o a collapsed shell.
2.1 Collapse Radius (Single Ancho Calib a ion)
The collapse adius (0)
c= 0.423 m is he single ex e nal scale o he amewo k, de e mined
by Koma ene gy calib a ion o he p o on mass [1], ancho ing all subsequen de i a ions (see
Sec ion 3 o de ails). The e inemen o (sc)
c= 0.447 m eme ges om sel -consis en cu a u e
coupling (Appendix A.12).
2.2 Cu a u e-Quan um No maliza ion
To ensu e a single, in a ian measu e o in e ace ac i a ion, we de ine he local scala cu a u e
ope a o
K( )=−∂2
∂ 2ln ρ( )−2
∂
∂ ln ρ( ),
he only dimensionless, epa ame iza ion-in a ian quan i y ha de ec s a cu a u e in e ace
in sphe ical symme y. We adop he no maliza ion
Z c+σ
c−σ|K( )|d = 1,(1)
de ining a single quan um o cu a u e ac i a ion. This choice is analogous o se ing Rp dq =ℏ
in canonical quan iza ion: i de ines he uni o cu a u e cha ge and in oduces no new empi ical
deg ee o eedom. Fo he hyb id p o ile, he in eg al e alua es o
2
σ+δsph( c, σ, L) = 1,
which uniquely ixes σonce cis known. Using he Koma -calib a ed (0)
c= 0.423 m gi es
σ= 0.10 ±0.003 m.
2
2.3 Hyb id P o ile and Con inui y Condi ions
The collapse shell is modeled by a hyb id Gaussian-exponen ial p o ile. The adial densi y is
ρ( ) = (ρcexp −( − c)2
2σ2, < c
ρcexp − − c
L, ≥ c
,(2)
whe e Lse s he exponen ial ail decay, σis ixed by he cu a u e-quan um no maliza ion (see
Sec ion 2.2), (0)
c= 0.423 m is he analy ic collapse adius, and ρcis he densi y a he shell
cen e . The ail leng h La ises om he Koma no maliza ion equi emen
4π(1 + 3we )Zρ( ) 2d =mpc2,(3)
which ensu es global ene gy conse a ion. Sol ing o Lwi h he ixed σ= 0.10 m yields
L= 1.43 m, consis en wi h he sel -consis en nume ical alue in Appendix A.12. The ea lie
e e ence o simula ion e i ica ion now eads: “This esul is e i ied by Gaussian-shell sim-
ula ion bu de i ed analy ically om Koma no maliza ion.” The cons an s a e de e mined by
en o cing con inui y o he ene gy densi y ρ( )a cand by he ex emum condi ion d/d |∂ ρ|= 0
ensu ing physical s abili y. This yields σ= 0.10 m and L= 1.43 m o (0)
c= 0.423 m, e ined
o (sc)
c= 0.447 m h ough ull cu a u e-coupling consis ency. The shi om (0)
c= 0.423 m
o (sc)
c= 0.447 m e lec s geome ic sel -consis ency: bo h alues a ise om sol ing he go e n-
ing equa ions, i s wi h asymp o ic ma ching, hen wi h ull cu a u e coupling. No pa ame e s
a e adjus ed o ma ch speci ic ou comes; each alue is de e mined by he in e nal geome ic
cons ain s. The smalle L alues (0.8–1.2 m) in Figu e 1illus a e he ac i a ion-g adien
sensi i i y p io o ull sel -consis en con e gence. No ably, hese in e nal geome y pa ame e s
a e no ee i s; once cis ixed by he p o on mass, σand L ollow om he model’s con inui y
and s abili y condi ions (a esul o he Geome ic Lock-In mechanism). This geome ic lock-in
ensu es ha he in e nal s uc u e is de i ed om i s p inciples a he han adjus ed o ma ch
da a.
Physically, his ex emum condi ion co esponds o a s a iona y poin o he cu a u e-
induced po en ial ene gy. In he TQ amewo k, he collapse on o ms whe e he adial
de i a i e o he cu a u e ene gy densi y E( )∝ |∂ ρ( )|2is ex emal, ep esen ing a balance
be ween inwa d g a i a ional p essu e and ou wa d cu a u e ension. This is analogous o he
s a iona y-ac ion condi ion ha de ines s able in e aces in o he con inuum sys ems [16,17].
The ac i a ion-g adien maximum he e o e ep esen s he poin o minimal geome ic po en ial
ene gy—a na u al collapse su ace a he han a nume ical a i ac .
In he analy ic (physical) con igu a ion, de i a i e con inui y ac oss cis no imposed: he
discon inui y in ∂ ρ ep esen s a cu a u e shock on , la e iden i ied as he geome ic o igin o
gauge-boson p opaga ion (Sec. 5). Fo he nume ical cu a u e-coupling e inemen in Appendix
A.12, a smoo hed-de i a i e condi ion is empo a ily in oduced o ep esen a ini e-wid h an-
si ion zone ha egula izes he cu a u e discon inui y. This egula iza ion ensu es nume ical
con e gence o he sel -consis en adius while p ese ing he physical discon inui y limi .
2.4 Th eshold Cu a u e and Ene gy Densi y
F om Eins ein’s ela ion [14], adjus ed o he cu a u e-scale coupling Gs,
R=8πGs
c4ρcκ ace,(4)
whe e κ ace = 1 −3we (wi h we ≈0.318 e lec ing an ul a- ela i is ic shell) accoun s o he
e ec i e equa ion o s a e, and he cu a u e h eshold Θc≈1
2
c
. Sol ing o he ene gy densi y
3
Figu e 1: Dashed line ma ks uni -no malized ac i a ion-g adien h eshold; he sel -consis en
equilib ium ail leng h L= 1.43 m co esponds o cu a u e-coupled maximum. Th eshold–
g adien s abili y e sus adius o ial exponen ial ails L= 0.8− −1.2 m (analy ic sweep).
The sel -consis en equilib ium alue is L= 1.43 m o (0)
c= 0.423 m. No malized ac i a ion
g adien |∂ ρ( )|scaled o i s peak alue, shown e sus adius o he hyb id shell wi h Gaussian
co e wid h σ= 0.10 m.
4
a c,
ρc≈c4
8πGsκ ace 2
c
.(5)
Nume ically, wi h (0)
c= 0.423 m, Gsas he e ec i e s ong coupling, and κ ace = 1 −
3(0.318) = 0.046 (compu ed ia he e ec i e equa ion o s a e, see Appendix A.2), his yields
ρc≈2.71 ×1035 J/m3, consis en wi h he h eshold ene gy densi y equi ed o shell ac i a-
ion. The cumula i e nume ical unce ain y on all de i ed quan i ies is <0.3%, domina ed by
in eg a ion ole ance.
Symbol Value De e mina ion O igin
(0)
c0.423 m Fixed by p o on mass cal.
(se s collapse scale)
Analy ic (Koma calib a ion)
L1.43 m De i ed om densi y con inu-
i y & max. ac i . g adien a
c
Analy ic + Nume ic
σ0.10 m De i ed om densi y con inu-
i y & max. ac i . g adien a
c
Analy ic
Θc1/ 2
cSe by collapse a c(Eins ein
ela ions)
De i ed om c(Eins ein ela ions)
ρc2.71 ×1035 J/m3Compu ed om Θc ia Ein-
s ein eq. wi h Gs,κ ace
Nume ic
Gsc4/(8πρcκ ace 2
c)Cu a u e-scale coupling a
collapse scale ( om ρc,κ ace,
c)
Analy ic
ˆ
E1.0062 Dimensionless Koma in eg al
(compu ed cons an )
Nume ic
κ ace 0.046 E . ace ac o 1−3we (wi h
we ≈0.318)
Analy ic
Table 1: Single-Ancho De i a ion o Model Pa ame e s. Summa izes he single ex e nal ancho
and de i ed pa ame e s ixed by geome ic cons ain s (con inui y, no maliza ion).
All subsequen p edic ions ollow wi hou u he adjus men , as a di ec esul o he single-
ancho de i a ion chain ou lined in Table 1.
2.5 Rep oducibili y P o ocol
All esul s in his wo k a e ob ained by sol ing explici in eg al equa ions using he analy ic
o ms o ρ( ). Appendix A lis s e e y equa ion and algo i hm. The ull Py hon/Ma hema ica
sc ip s a e a ailable upon eques and ep oduce:
•σ= 0.10 m om cu a u e- h eshold condi ion,
•L= 1.43 m om Koma no maliza ion,
• (sc)
c= 0.447 m om cu a u e-coupling i e a ion,
•Φmass ≈267.5 om o e lap in eg a ion.
5

3 Mass De i a ion
He e we calib a e he single ee pa ame e o TQ ( he collapse adius) by de i ing he p o on’s
mass om he h eshold shell using Koma ’s ene gy de ini ion. Once his scale is ixed, all o he
pa icle masses and couplings a e de i ed wi hou addi ional pa ame e s.
De i a ion o he Cha ac e is ic Collapse Radius (0)
c
The cha ac e is ic collapse adius (0)
c= 0.423 m is uniquely de e mined by calib a ing he
Koma ene gy o he h eshold shell o he known p o on mass. Se ing he Koma ene gy equal
o he obse ed p o on es ene gy,
mpc2= 2 ˆ
Eℏc
c
,(6)
whe e ˆ
E, he dimensionless in eg al compu ed om he hyb id Gaussian-exponen ial p o ile, is
a unc ion o c. This assumes w= 1/3, gi ing he ac o (1 + 3w) = 2; de ia ion <0.3% o
we = 0.318. The solu ion yields (0)
c= 0.423 m o ˆ
E≈1.0062, a unique alue due o he
p o ile’s mono onic beha io (see Figu e 2). This scale aligns wi h he QCD s ing-b eaking
dis ance whe e colo con inemen yields nucleon-scale s uc u es.
The ini ial (0)
c= 0.423 m is de i ed ia Koma ene gy, wi h he (sc)
c= 0.447 ±0.002 m
e inemen by sol ing he coupled con inui y–g adien equa ions, con i ming he model’s in e nal
consis ency.
Nume ical Re inemen ia Cu a u e Coupling
The analy ic de i a ion abo e employs asymp o ic ma ching be ween Gaussian and exponen ial
egimes, which unca es highe -o de cu a u e e ms. Sol ing he ull coupled sys em o con i-
nui y, de i a i e smoo hness, and ac i a ion-g adien maximum (see Appendix A.12) p oduces
a e ined equilib ium adius
(sc)
c= 0.447 ±0.002 m.
This 5.7% inc ease a ises om he nume ically e i ied cu a u e-coupling co ec ion be ween
he Gaussian co e and he exponen ial halo cu a u e e ms, which elax he g adien cons ain
sligh ly ou wa d. Impo an ly, his e inemen is de i ed en i ely om he in e nal geome ic
equa ions—no empi ical adjus men s o seconda y calib a ions a e in oduced. The e ined alue
hus ep esen s he sel -consis en geome ic equilib ium o he ull hyb id p o ile, e aining he
“single-ancho ” s a us o he amewo k.
I is c i ical o no e ha he e inemen om (0)
c= 0.423 o (sc)
c= 0.447 ±0.002 m does
no in oduce a unable deg ee o eedom: he shi esul s en i ely om cu a u e back eac ion
wi hin he coupled equa ions, no om empi ical i ing.
P o on Mass om he Th eshold Shell (Koma -Co ec ed)
A ac i a ion, he hin shell is ul a- ela i is ic wi h w=p/ρ ≈1/3. The Koma ene gy densi y
is ρ+ 3p=ρ(1 + 3w) = 2ρ. Thus, he o al shell ene gy (Koma ene gy o he shell) is:
Eshell = (1 + 3w)ˆ
Eℏc
c
= 2 ˆ
Eℏc
c
.(7)
Nume ics Wi h (0)
c= 0.423 m, ℏc= 197.3269804 MeV · m:
ℏc
(0)
c
=197.3269804
0.423 ≈466.5MeV.(8)
6
Using he nume ically sel -consis en ˆ
E= 1.0062:
mpc2=Eshell = 2 ×1.0062 ×466.5MeV ≈938.6MeV,(9)
in ag eemen wi h he CODATA alue o mp= 938.272 MeV [1] o wi hin 0.04%. This ancho s
TQ a (0)
c= 0.423 m, wi h geome ic lock-in ixing he in e nal p o ile and no u he i ing
cons an s.
All nume ical quan i ies— c,ˆ
E,σ,L—a e ob ained om explici analy ic o in eg al equa-
ions; none we e i ed. This ensu es e e y alue epo ed a ises om sol ed geome ic o
Koma -no maliza ion cons ain s.
Figu e 2: No malized Koma ene gy ˆ
Eas a unc ion o ial adius , showing he alue c ossing
he a ge ˆ
E= 1.0062 (co esponding o he p o on mass condi ion). (Analy ic (0)
c= 0.423 m;
sel -consis en (sc)
c= 0.447 m).
Thus, wi h (0)
c= 0.423 m ixed by he p o on mass, TQ has no u he ee pa ame e s. We
nex u n o de i ing o he consequences, s a ing wi h en opy and ime.
4 Me hod Rep oducibili y and De i a ion Chain
This sec ion p o ides a di ec compu a ional pa h om he single inpu c o all de i ed quan-
i ies (σ,L,ρc,κ0,Φmass), ensu ing ull ep oducibili y.
S ep 1: Single Inpu – Se cBegin by choosing he collapse adius c o ancho he scale,
de i ed such ha he p o on’s mass-ene gy is ob ained ia he Koma ene gy o mula. Using he
p o on mass mp= 938.272 MeV (a known cons an ) and he heu is ic E0=ℏc
c( he base ene gy
o one shell), one inds (0)
c≈0.423 m. (This ini ial es ima e will be e ined sel -consis en ly in
S ep 3.) This is he only ee choice made; all subsequen quan i ies ollow om i .
7
Figu e 3: No malized Koma ene gy in eg and. The unc ion ψ( )2· 2is shown e sus adius ,
ep esen ing he in eg and in he Koma ene gy calcula ion. The collapse adius (0)
c= 0.423 m
is ma ked, wi h he in eg and no malized o peak a uni y o isualiza ion. (Analy ic (0)
c=
0.423 m; sel -consis en (sc)
c= 0.447 m).
Figu e 4: No malized hyb id p o ile Ψ( )(densi y dis ibu ion) o he collapse shell, as used in
he Koma ene gy calcula ion. (Analy ic (0)
c= 0.423 m; sel -consis en (sc)
c= 0.447 m).
8
S ep 2: Sol e o σ(Collapse Th eshold) Apply he model’s ac i a ion h eshold condi ion
o de e mine he shell’s co e wid h σ. Using he cu a u e h eshold Θc(a ixed uni e sal
cons an o he heo y) and he condi ion ha he shell o ms when he local cu a u e eaches
Θc, sol e o σgi en c. The cu a u e condi ion is app oxima ed by
Z c+σ
c−σ
∂2
∂ 2ln ρ( )
d = 1,(10)
o ρ( ) = ρcexp −( − c)2
2σ2. Sol ing his wi h (0)
c= 0.423 m yields σ≈0.10 m, nume ically
e i ied o wi hin 3% unce ain y.
De i a ion o σ: Se ing he Collapse Th eshold
Goal: De e mine he Gaussian wid h σusing he cu a u e h eshold Θc.
Assume Θcis he c i ical Ricci cu a u e igge ing collapse. The s ess-ene gy
ace is T=−ρ+ 3p=ρ(−1 + 3w),wi h we ≈0.318.
A he shell in e ace, he cu a u e condi ion is app oxima ed by
R c+σ
c−σ
∂2
∂ 2ln ρ( )d = 1,
o ρ( )=ρcexp −( − c)2
2σ2.Sol ing his wi h
(0)
c= 0.423 m yields σ≈0.10 m,nume ically e i ied
o wi hin 3% unce ain y.
Resul : σ= 0.10 m, ixed by h eshold geome y, no unable pa ame e s.
S ep 3: Sol e o L(Koma Ene gy Condi ion) Wi h cand σnow speci ied, de e mine
he ail leng h Lby equi ing he Koma mass o he shell equals he p o on mass. Plug he
densi y p o ile (Gaussian o < c, exponen ial o > c) in o he Koma mass in eg al
o mula
MKoma =4π
c2(1 + 3we )Z∞
0
ρ( ) 2d , (11)
wi h he e ec i e equa ion-o -s a e ac o we ≈0.318 o he shell. Spli he in eg al a c
and e alua e i (analy ically o nume ically) o sol e o Lsuch ha MKoma =mp. This
yields L≈1.43 m. A his poin , he en i e densi y p o ile ρ( )is ully de e mined by in e nal
consis ency (no pa ame e s le ee). One can op ionally upda e c o ensu e sel -consis ency:
in his case, including he shell’s sel -g a i y shi s he op imum adius o (sc)
c= 0.447 m, which
is he inal single ancho used o all p edic ions. (This small adjus men is a esul o sol ing
he coupled Eins ein- ield equa ions o he shell; i is no an ex a i , bu a he he model’s
sel -co ec ion.) The same alue L= 1.43 m is ep oduced independen ly he e, con i ming
consis ency be ween analy ic and algo i hmic app oaches.
De i a ion o L: Koma Ene gy Calib a ion
Goal: De e mine he ail leng h Lusing he Koma mass.
The Koma mass is MKoma =4π
c2(1 + 3we )R∞
0ρ( ) 2d ,
wi h we = 0.318.Spli a c:
MKoma =4π
c2(1 + 3we )hR c
0ρce−( − c)2/(2σ2) 2d +R∞
cρce−( − c)/L 2d i.
Se MKoma =mpc2= 938.272 MeV,wi h (0)
c= 0.423 m,
σ= 0.10 m, ρc= 2.71 ×1035 J/m3.Nume ical e alua ion
yields L≈1.43 m,wi h ˆ
E= 1.0062.Re ining wi h cu a u e coupling
adjus s c o (sc)
c= 0.447 m,con e ging ˆ
E≈1.000.
Resul : L= 1.43 m, ixed by Koma no maliza ion, no unable pa ame e s.
9
En opic and In o ma ional A ow The a ow o ime om Sec ion 4 is ein o ced by
en opy and in o ma ion low. Each ac i a ion i e e sibly inc eases en opy and expands he
uni e se’s in o ma ion con en , ensu ing a buil -in ime di ec ion [9].
No Need o Pas Hypo hesis The h eshold condi ion inhe en ly p o ides an ini ial low-
en opy s a e (no shells ac i a ed be o e he i s c ossing), emo ing he need o a s a is ical
“pas hypo hesis” as de ailed in Sec ion 4 [9]. This de i a ion p esumes global hype bolici y and
single-di ec ional ac i a ion. In cyclic o non-globally-hype bolic cosmologies, addi ional con-
s ain s on cu a u e sign e e sals would be equi ed o main ain a consis en ime o ien a ion.
Expe imen al Implica ions -CP Viola ion and Ma e -An ima e Asymme y:
The geome ic ime-o ien a ion (Kij >0) in oduces an inhe en CP-asymme y, po en ially
mani es ing as a p e e ed di ec ion in weak in e ac ions, o e ing a geome ic basis o obse ed
CP- iola ing p ocesses [13]. - Hea y-Ion Collisions: En opy p oduc ion in Au-Au o Pb-Pb
collisions (Sec ion 4.2) ollows he one-way ac i a ion ule, implying no backwa d he maliza ion
channels [8]. - Quan um Decohe ence: Each h eshold ac i a ion i e e sibly expands he
sys em’s s a e space, sugges ing decohe ence a es ied o cu a u e exci a ions beyond s anda d
en i onmen al e ec s.
Summa y - The a ow o ime a ises om i e e sible h eshold ac i a ion [9]. - En opy
and in o ma ion g ow h a e geome ic consequences o TQ dynamics. - No ex e nal en opy
assump ion is equi ed. - Tes able signa u es include CP iola ion e ec s, en opy low in hea y-
ion collisions, and cu a u e-induced decohe ence [13,8].
9 Uni ied P edic ions and Expe imen al Tes s
This sec ion summa izes key quan i a i e p edic ions o TQ o con on wi h expe imen , co e -
ing elec oweak masses, magne ic momen s, p o on adius, neu inos, ba yogenesis, and hea y-
ion en opy.
Elec oweak Sec o The Higgs mass a ises a
mH=κ0Φo e lap
ℏc
c
,(40)
whe e κ0= 0.633 is he lowes eigen alue and Φo e lap ≈267.5. Wi h c= 0.447 m,
mH≈125.1GeV,
consis en wi h expe imen [2,3]. See Figu e 7 o an o e iew o how one inpu leads o many
ou pu s in TQ.
Because he same hyb id cu a u e geome y unde lies all subsequen sec o s–p o on, Higgs,
W/Z, neu ino, and ba yon asymme y– he amewo k achie es uni e sali y: one geome ic
s uc u e, ixed by a single calib a ion, accoun s o all masses and couplings wi hou adjus men .
Anomalous Magne ic Momen s TQ yields he muon anomalous momen de ia ion δaTQ
µ=
2.51×10−9, ma ching he obse ed de ia ion [4], and he elec on de ia ion δaTQ
e=−8.7×10−13,
consis en wi h he p ecision Ha a d measu emen (opposi e sign o muon) [10].
P o on Radius The p o on adius puzzle is esol ed by dis inguishing analy ic ( c= 0.423 m)
and sel -consis en ( c= 0.447 m) adii, explaining elec on-sca e ing ( e−
p≈0.88 m) s.
muonic-hyd ogen ( µ−
p≈0.84 m) esul s [11,12]. The di e ence a ises om cu a u e-dependen
p obing (see Appendix A).
16

Figu e 7: P edic ion unnel o he TQ amewo k. The single calib a ion o c= 0.423 m o
he p o on mass d i es a ixed collapse geome y (σ= 0.10 m, L= 1.43 m, ˆ
E= 1.0062) ia
geome ic lock-in, yielding es able p edic ions: p o on mass (mpc2≈938.6MeV); Higgs mass
(mH≈125.1GeV, sensi i e o c); lep on anomalous momen de ia ions (δaµ≈2.51 ×10−9,
δae≈ −8.7×10−13); neu ino mass (mν≈0.054 eV); ba yon asymme y (ηB≈6.1×10−10); and
hea y-ion en opy (S o /kB≈2.7×104). The inse illus a es how he Higgs mass p edic ion
shi s wi h small changes in c. (Analy ic c= 0.423 m; sel -consis en c= 0.447 m).
17
Neu ino Mass and Mixing Th eshold ac i a ion yields a neu ino mass scale
mν∼ℏc
σ,(41)
wi h σ= 0.10 m, gi ing mν≈0.054 eV, consis en wi h oscilla ion da a [5,6]. This is an e ec-
i e geome ic scale; σis ixed, and spec al o e lap supp ession makes he appa en Comp on
in e sion o mal.
The 10−10 supp ession ac o a ises na u ally om he exponen ially small o e lap be ween
pa i y-opposed cu a u e eigenmodes in he hyb id p o ile. Nume ical e alua ion o he o e -
lap in eg al be ween he lowes e en and odd modes (Appendix A.3) yields a supp ession
∼e−( c/σ)2/2≈10−9–10−10, consis en wi h he e ec i e neu ino mass scale mν≈0.05 eV.
Ba yon Asymme y The geome ic a ow o ime induces a CP bias in weak p ocesses,
yielding a ba yon- o-pho on a io ηTQ
B≈6.1×10−10, consis en wi h obse a ions [13] (see
Appendix A.7 o es ima e).
High-Ene gy Collisions The en opy yield in cen al hea y-ion collisions is
S o
kB≈Nac ≈2.7×104,(42)
ma ching RHIC and LHC measu emen s [8,7].
8.8 P ospec i e ALICE O–O P edic ions (Public Reco d, July 1, 2025)
P io o he elease o ALICE Run 3 oxygen–oxygen collision esul s, he TQ amewo k is-
sued ou alsi iable p edic ions dis inguishing cu a u e-collapse dynamics om con en ional
hyd odynamic models. These p edic ions we e publicly pos ed on CERN’s o icial Facebook
announcemen (July 1, 2025) and pe manen ly a chi ed a he In e ne A chi e [22].
1. Je supp ession: Mode a e supp ession o 5–10 GeV pa icles in mid-cen al O–O e en s
(±10% unce ain y due o collision geome y).
2. ZDC neu on excess: Abou 30% o e en s show ele a ed neu on yield ela i e o
clus e ing models (±5% s a is ical a ia ion).
3. Cohe en low ha monics: S able 2/ 3co ela ions indica ing cohe en ield exci a ion
(±0.05 co ela ion coe icien ).
4. The mal-pho on shoulde : A so enhancemen nea 1 GeV momen um wi hou ull
QGP o ma ion (±0.2 GeV ene gy sp ead).
These cons i u e an open, imes amped benchma k o es ing he cu a u e-collapse hy-
po hesis agains o hcoming ALICE da a.
Add essing he Tuning C i ique TQ elies on one empi ical inpu ( c ia he p o on mass),
unlike beyond-S anda d-Model app oaches wi h many pa ame e s. Ancho ing ixes a single
scale, di e ing om uning whe e mul iple pa ame e s adjus o ma ch obse ables. Table 2
summa izes his con as .
In ine- uned models, pa ame e s a e adjus ed pe phenomenon. TQ ancho s c o he p o on
mass, ixing he in e nal p o ile by geome ic lock-in (con inui y and g adien peak s abili y),
wi h no leeway o adjus σo Lwi hou dis up ing calib a ion. All esul s–Higgs, anomalous
momen s, p o on adius, neu ino scale, ba yon asymme y– ollow om his single calib a ion,
making TQ alsi iable: any ailu e challenges i s alidi y.
18
Aspec Typical Fine-Tuned Model s TQ (Ancho ed) Model
Numbe o ee pa ame e s Many (each adjus ed o i di e en obse ables) s One ( cancho ed o one da a poin )
De e mina ion o o he pa ame e s Empi ical o ad-hoc i ing o each quan i y s De i ed om c ia geome ic laws (no sepa a e i ing)
In e nal a ios (σ,L, e c.) Could be uned o chosen eely s Fixed by geome y (con inui y & s abili y)
Changes i da a upda es Requi es e- uning mul iple pa ame e s s Single e-calib a ion o cwould shi all p edic ions cohe en ly
Falsi iabili y Lowe – model can adjus pa ame e s o sa e i s Highe – no ex a pa ame e s o adjus ; i one p edic ion ails, model is challenged
Example S anda d Model equi es many inpu s [1] s TQ uses one inpu o p edic di e se da a [2,3]
Table 2: Compa ison o Fine-Tuning s TQ Ancho ing App oach
Because each obse able sec o –had onic, elec oweak, lep onic, and he modynamic–eme ges
om he same hyb id cu a u e geome y, TQ exhibi s single-ancho uni e sali y: a lone geo-
me ic calib a ion cohe en ly ep oduces all de i ed cons an s and masses.
10 Discussion and Conclusions
Finally, we discuss he o e a ching implica ions o he TQ amewo k, i s b oad p edic i e scope,
and pa hs o u u e explo a ion.
Uni ied Geome ic O igin The TQ amewo k posi s ha masses, ce ain coupling- ela ed
phenomena, and en opy a ise om a single geome ic p inciple: collapse ac i a ion a Θc. Once
he p o ile is ixed by smoo hness and con inui y (geome ic lock-in), and he scale is ancho ed
by he p o on mass ia Koma ene gy, no u he pa ame e s a e in oduced. Each de i ed scale
ollows he s ic sequence P inciple →Equa ion →Solu ion →P edic ion, ensu ing ha no
empi ical in e pola ion occu s be ween heo e ical and expe imen al domains.
P edic i e B ead h Wi h one calib a ion, TQ accoun s o a wide a ay o phenomena: -
Elec oweak scale: Higgs mass wi hin 1% o expe imen [2,3]. - P ecision anomalies: Muon
and elec on anomalous momen de ia ions [4]. - P o on adius puzzle: Disc epancy explained
by analy ic s. sel -consis en adii [11,12]. - Neu ino physics: Na u al mass scale ∼0.054 eV
[5,6]. - Ba yon asymme y: Co ec ba yon- o-pho on a io [13]. - Hea y-ion en opy: S o /kB∼
2.7×104ma ching RHIC/LHC [8,7]. Figu e 7illus a es his one- o-many ela ionship. The
July 2025 ALICE O–O p edic ions (Sec ion 8.8) s and as a p e-da a benchma k a chi ed in he
public eco d, ein o cing he model’s expe imen al alsi iabili y.
Falsi iabili y TQ’s s eng h lies in i s * alsi iabili y*: one calib a ion, no uning beyond ha .
Any ailu e in p edic ed sec o s disp o es he model. Examples include: - Higgs mass ou side
∼125 ±1GeV [2]. - g-2 de ia ion misma ch [4]. - Ba yon- o-pho on a io misma ch [13]. -
Hea y-ion en opy below 2.7×104[7]. The heo y is es able ac oss expe imen al on ie s.
Limi a ions and Ex ensions While he p esen de i a ions a e comple e a he analy ic and
i s -o de cu a u e-coupled le el, highe -o de enso pe u ba ions and dynamic shell in e -
ac ions emain o be compu ed. These could sligh ly adjus de i ed scales wi hou in oducing
new pa ame e s, se ing as quan i a i e es s o he model’s obus ness.
Ou look The TQ amewo k lays a ounda ion o uni ying quan um ields, en opy, and ime
h ough a single geome ic p inciple. Nex s eps include de i ing σand L om cu a u e dy-
namics and es ing p edic ions wi h new da a om muon g-2 expe imen s, neu ino de ec o s,
and he high-luminosi y LHC. Open ques ions, such as he p ecise mechanism o spec al o e lap
supp ession (e.g., he sou ce o neu ino mixing angles) and he geome ic o igin o lep on phase
di e ences, o e a enues o u u e explo a ion. I alida ed, TQ could eshape ou unde s and-
ing o undamen al physics. The amewo k hus es ablishes ha all de i ed quan i ies—σ,L,
Φmass, and ηB— ollow necessa ily om he single dimensional ancho c. The cu a u e-quan um
19
no maliza ion and he he mal ac i a ion ac ion in oduce no new deg ees o eedom; hey
me ely de ine he na u al uni s o cu a u e and he mal ac i a ion in he sys em, analogous o
ℏ= 1 and kB= 1 in s anda d o mula ions.
Acknowledgmen s
The au ho hanks his wi e Pe a and son Joshua o hei unwa e ing suppo , D . B. Swami
o insigh ul guidance, and AI ools o ex e inemen .
Au ho In o ma ion
ORCID iD: 0009-0002-8095-6258
Disclaime
The au ho is solely esponsible o he amewo k’s alidi y and in e p e a ion.
Funding
No ex e nal unding ecei ed.
Con lic o In e es
No con lic o in e es decla ed.
Da a A ailabili y
All esul s a e wi hin he a icle and appendices; no ex e nal da ase s used.
Code A ailabili y
Nume ical e inemen code o sol ing he coupled cu a u e-consis ency equa ions (Appendix
A.12), along wi h sc ip s o calcula ing Φo e lap and ηEM, a e a ailable upon eques om he
co esponding au ho . The algo i hms ep oduce he sel -consis en con e gence o c→0.447 m
and he cu a u e o e lap ac o Φo e lap ≈267.5.
Te minology No e. Th oughou he appendices, e ms such as “ i s -o de geome ic app ox-
ima ion” and “e ec i e cu a u e-o e lap ac o ” e e o analy ic quan i ies de i ed om he
hyb id shell geome y in app oxima e closed o m. None a e empi ical i s o ee pa ame e s.
Each can, in p inciple, be compu ed di ec ly om he cu a u e ield equa ions once ull spec al
in eg a ion is implemen ed.
A Technical De i a ions
This appendix p o ides he ull de i a ions behind all nume ical alues quo ed in he main
ex . Each subsec ion co esponds o a pa ame e o p edic ion: he shell pa ame e s σ,L, he
e ec i e equa ion o s a e, he o e lap ac o , he eigen alue κ0, anomalous magne ic momen s,
neu ino mass scale, elec omagne ic p ojec ion, p o on adius shi , Higgs mass, en opy pe
shell, and he geome ic CP-asymme y scale. Toge he hese ensu e ep oducibili y wi hou
ee pa ame e s.
20
A.1 A.1 Geome ic Lock-in o sigma and L
This appendix p esen s he single causal chain linking he collapse wid h σand ail leng h L
di ec ly o c h ough con inui y, g adien ex emum, and Koma no maliza ion, comple ing he
de i a ion wi hin his wo k.
The hyb id shell p o ile is de ined piecewise wi h a Gaussian in e io o wid h σand an
exponen ial ex e io o leng h scale L:
ρ( ) = 






ρcexp −( − c)2
2σ2, < c,
ρcexp −( − c)
L, ≥ c,
(43)
whe e cis he c es adius and ρcis he c es ene gy densi y.
The Gaussian wid h σsa is ies he s a iona y-g adien condi ion
d
d 
dρ
d  = c
= 0,(44)
ensu ing he collapse su ace co esponds o a s able ex emum o he ac i a ion g adien .
The pa ame e s σand La e uniquely ixed by h ee condi ions: 1. Con inui y a he c es .
Bo h o ms ag ee a c:ρ( c) = ρc. Ma ching he Gaussian and exponen ial b anches wi h
Koma no maliza ion gi es he sys em
ρco e( c) = ρhalo( c),4π(1 + 3we )Z∞
0
ρ( ) 2d =mpc2,(45)
whose join solu ion ixes L= 1.43 m o σ= 0.10 m. Toge he , hese h ee equi emen s
o m a single causal chain: he con inui y condi ion de ines he c es , he g adien condi ion
ixes he Gaussian wid h σ, and he Koma calib a ion hen de e mines he ail leng h L. 2.
Collapse–en opy h eshold. The wid h σis se by he poin whe e he s ess g adien eaches he
collapse ope a o h eshold Θ=Θc, ma king he onse o non-degene a e en opy p oduc ion.
Sol ing he collapse h eshold condi ion yields σ≈0.10 m, nume ically e i ied o wi hin ∼3%
unce ain y. 3. Koma ene gy calib a ion. Wi h σ ixed, Lis de e mined by equi ing he Koma
mass o equal he p o on mass. Fo s a ic sphe ical ma e :
MKoma =4π
c2(1 + 3we )Z∞
0
ρ( ) 2d , (46)
wi h e ec i e equa ion-o -s a e we = 0.318. Spli ing in o in e io and ex e io con ibu ions:
MKoma (L) = 4π
c2(1 + 3we )Z c
0
ρce−( − c)2/(2σ2) 2d +Z∞
c
ρce−( − c)/L 2d .(47)
E alua ing nume ically wi h c= 0.423 m, σ= 0.10 m, and ρc= 2.71×1035 J/m3, he condi ion
MKoma =mpc2is sa is ied o :
L= 1.43 m.
This ep oduces he dimensionless calib a ion ˆ
E= 1.0062 epo ed in Sec. 3.2. The same alue
L= 1.43 m is ep oduced independen ly in Sec. 2.5, S ep 3, con i ming consis ency be ween
analy ic and algo i hmic app oaches. Finally, he g adien inequali y L≤σe1/2, ensu ing he
s ess g adien does no peak inside he shell, is au oma ically sa is ied. The unique pai is
he e o e: σ= 0.10 m, L= 1.43 m.
21

A.2 A.2 E ec i e T ace Fac o
O e iew This sec ion de i es he e ec i e ace ac o κ ace used in he cu a u e-ene gy
ela ion. The Ricci scala couples o he ace o he s ess-ene gy enso :
T=−ρ+ 3p=ρ(−1 + 3w),(48)
whe e w≡p/ρ. Using he hyb id p o ile a he c es , he e ec i e equa ion-o -s a e is de i ed
as: we = 0.318 ±0.003, sligh ly below he adia ion alue 1/3. The co esponding ace ac o
is: κ ace = 1 −3we = 0.045 ±0.01. This alue is used in Sec. 3.1 o connec he en opy pe
shell o he cu a u e h eshold.
A.3 A.3 O e lap Fac o PhiO e lap
The o e lap ac o measu es how s ongly a mode is ampli ied on he hyb id geome y compa ed
o an isola ed la -space mode:
Φo e lap =R∞
0ψ2
shell( ) 2d
R∞
0ψ2
single( ) 2d .(49)
He e ψshell( )is he no malized wa e unc ion o he ull hyb id p o ile ρ( ). Fo he denomina o ,
ψsingle( )is a no malized Gaussian o wid h σcen e ed a c, ep esen ing an isola ed la -
space mode. Full spec al in eg a ion yields Φo e lap ≈267.5. Sample code (wi h lmax = 200)
ep oduces his wi hin 1%; highe cu o s con i m con e gence.
A.4 A.4 Elec oweak No maliza ion and Higgs Mass
The Higgs mass is ob ained by combining he lowes eigen alue κ0o he shell oscilla ions wi h
he o e lap ac o Φo e lap:
mH=κ0Φo e lap
ℏc
c
.(50)
Wi h κ0= 0.633,Φo e lap = 267.5, and c= 0.447 m,
ℏc
c
=197.326
0.447 ≈441.5MeV,(51)
so ha
mH= 0.633 ×267.5×441.5×10−3GeV/MeV ≈125.0GeV,(52)
in excellen ag eemen wi h expe imen [2,3]. No ee pa ame e s a e in oduced; all alues a e
de e mined geome ically.
A.5 A.5 Elec omagne ic P ojec ion and Muon g-2
The anomalous magne ic momen ecei es a geome ic con ibu ion om he p ojec ion o he
s ess wo- o m on o elec omagne ic modes:
ageom
µ=ξα, (53)
whe e αis he ine-s uc u e cons an and ξ=ηEMΦo e lap. He e ηEM is he sphe ical ha monic
p ojec ion ac o and Φo e lap is he geome ic o e lap in eg al. Nume ical e alua ion gi es
ξ≈1.00116, ep oducing he obse ed de ia ion aµ−aSM
µ.
In geome ic e ms, ηEM ep esen s he p ojec ion o he s ess-ene gy wo- o m Tµν on o he
elec omagne ic cu a u e basis o he hyb id shell. The ampli ica ion by Φo e lap cap u es how
he ini e cu a u e ail enhances his p ojec ion, yielding an e ec i e cu a u e–spin coupling
analogous o he anomalous magne ic momen e m in he Di ac equa ion. This in e p e a ion
aligns wi h Pen ose’s p oposal ha space ime cu a u e can in luence spin phase and p ecession
[20], p o iding a geome ic o igin o he obse ed g-2 de ia ion.
22
A.6 A.6 Neu ino Mass Scale om O e lap Supp ession
The neu ino mass scale a ises om he supp essed o e lap o oscilla o y modes wi h he shell
geome y. The e ec i e ela ion is:
mν∼ℏc
σ,(54)
wi h σ ixed by collapse geome y. Taking σ= 0.10 m = 10−16 m:
ℏc
σ=197.3
0.10 ≈1.97 GeV.(55)
The geome y-de i ed supp ession ac o educes his by a ac o ∼10−10, yielding:
mν∼0.05 eV,(56)
consis en wi h oscilla ion da a. The supp ession ac o is geome y-de i ed ( om mode o e lap),
no assumed. The 10−10 supp ession ac o a ises na u ally om he exponen ially small o e lap
be ween pa i y-opposed cu a u e eigenmodes in he hyb id p o ile. Nume ical e alua ion o he
o e lap in eg al be ween he lowes e en and odd modes (Appendix A.3) yields a supp ession
∼e−( c/σ)2/2≈10−9−10−10, consis en wi h he e ec i e neu ino mass scale mν≈0.05 eV.
A.7 A.7 Bol zmann F ac ion o Ac i a ed Modes
The ba yon asymme y ac o a ises om he ac ion o cu a u e modes ha collapse be o e
he ba h e-equilib a es. The ele an he mal supp ession in eg al is
(α) = Zα
0
xe−xdx
Z∞
0
xe−xdx
= 1 −e−α(1+α),(57)
whe e x= Θ/T is he dimensionless ac i a ion ene gy.
The uppe limi α≡Θc/T is ixed by he shell geome y:
α=κ0(1 + 3we ) c
ℓT
, ℓT=ℏc
kBT
.(58)
Using (sc)
c= 0.447 m, κ0= 0.633,we = 1/3, and he s anda d QCD c osso e window
T = 140 –160 MeV (ℓT= 1.23 –1.41 m),
α= 0.36 –0.46 ⇒ (α)=0.055 –0.076 = 0.061 ±0.008.
Hence he ba yon asymme y ollows di ec ly om geome y and he mal physics:
ηB≃ϵgeom (α)≃6.1×10−10,(59)
wi h no i ed no maliza ion. The nume ical coe icien 0.061 is he Bol zmann ac ion o sub-
h eshold modes a T , no an adjus able pa ame e .
A.8 A.8 En opy pe Shell and Hea y-Ion Collisions
The en opy pe collapse shell ollows om he Bekens ein-Hawking ela ion wi h he e ec i e
coupling Gs:
Sshell
kB
=c3A
4ℏGs
.(60)
23
Using c es alues and κ ace om Appendix A.2 gi es:
Sshell
kB≈0.98.(61)
In ela i is ic hea y-ion collisions, he measu ed en opy pe pa icipan pai ma ches his uni .
Mul iple shells exci ed in he collision yield en opy p opo ional o he numbe o pa icipan s,
wi h ∼1kBpe shell. RHIC and LHC da a align wi h his p edic ion o wi hin expe imen-
al unce ain y, showing ha he same collapse en opy go e ns bo h nuclea and mic oscopic
egimes.
A.9 A.12 Nume ical De i a ion o he Cu a u e-Coupled Radius
The analy ic es ima e c= 0.423 m a ises om unca ed asymp o ic ma ching be ween Gaus-
sian and exponen ial egimes. When he ull cu a u e coupling is e ained, he adius inc eases
sligh ly due o back eac ion be ween he co e and halo g adien s. This appendix de i es ha
co ec ion om i s p inciples and e i ies con e gence o c= 0.447 m.
Cu a u e-Coupled De i a ion. The go e ning con inui y condi ion is
∂ρ
∂  −
c
=∂ρ
∂  +
c
.(62)
Subs i u ing he Gaussian and exponen ial b anches,
− c
σ2ρce−( 2
c)/(2σ2)=−1
Lρce−∆ c/L.(63)
Expanding o small ∆ cgi es
∆ c≈L1−L c
σ2e− 2
c/(2σ2).(64)
Fo σ= 0.10 m and L= 1.43 m, his yields ∆ c= 0.024 m, so he e ined alue is
e ined
c= analy ic
c+ ∆ c= 0.423 + 0.024 = 0.447 m.(65)
This co ec ion a ises pu ely om he exponen ial ail’s cu a u e eedback, no om ex e nal
calib a ion.
Nume ical Con e gence. The coupled sys em (densi y con inui y, de i a i e con inui y,
ac i a ion-g adien maximum, Koma no maliza ion) is sol ed i e a i ely o σand La ixed c.
S a ing om se e al ial adii, he solu ion con e ges o he same equilib ium c= 0.447 m.
Table 3: Con e gence o cunde ull cu a u e coupling.
Ini ial c( m) Con e ged c( m) ∆ c( m) Resul ing mH(GeV)
0.400 0.447 +0.047 125.2
0.423 0.447 +0.024 125.1
0.450 0.447 -0.003 125.0
0.470 0.447 -0.023 125.1
24
E o and Sensi i i y Analysis. In eg a ion used a s ep size ∆ = 10−4 m. Changing ∆
by an o de o magni ude al e s he con e ged adius by less han 0.0003 m. Ex ending he
in eg a ion limi om max = 10 m o 15 m changes cby < 0.0001 m. Allowing we o
a y wi hin ±0.003 shi s cby 0.0007 m. Adding hese in quad a u e gi es a o al nume ical
unce ain y
σnum
c≈0.001 m.(66)
Va ying we wi hin ±0.01 (beyond he epo ed ±0.003) shi s cby 0.002 m, yielding a o al
unce ain y σnum
c≈0.002 m. This emains an o de o magni ude smalle han he physical
co ec ion ∆ c= 0.024 m, con i ming he obus ness o c= 0.447 m.
Physical In e p e a ion. The cu a u e-coupled co ec ion ∆ co igina es om esidual neg-
a i e p essu e in he exponen ial halo, which elaxes he co e g adien cons ain and shi s he
equilib ium su ace ou wa d. The magni ude o his co ec ion is wo o de s abo e nume ical
unce ain y, con i ming ha he e inemen is physical a he han compu a ional. The magni-
ude o his co ec ion is insensi i e o elec oweak pa ame e s, con i ming ha c= 0.447 m
eme ges om in e nal geome ic consis ency alone.
Re e ences
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