EIC Reading Guide & E a a:
P e-Th eshold Collapse and How o Read he “Dense
Fo mulas”
(Non-Ope a ional Cla i ica ion)
Takao Koizumi
Independen Resea che , Japan
[email p o ec ed]
No embe 5, 2025
Abs ac
This non-ope a ional no e consolida es cla i ica ion i ems and eading ules o he En opy-
Induced Collapse (EIC) amewo k. I o malizes he p e- h eshold iming o in e en ion (app oach-
om-below a he bounda y), ames analyses on he in e al be o e i s con ac wi h he h esh-
old, and explains how o ead he single-page “dense o mulas” ac oss he modynamic, quan um-
in o ma ion, s ochas ic/non-Ma ko , and iden i iabili y laye s. No algo i hms, p ocedu es, code,
o lab p o ocols a e p o ided. The sole aim is o educe mis eadings while p ese ing esea ch
sa e y. Public ques ions a e welcome a he symbol/de ini ion le el; ep oducibili y-o ien ed
eques s will no be add essed.
Con en s
1 Scope and Sa e y Policy 4
1.1 Non-ope a ional s ance ................................. 4
1.2 Dual-use isk managemen ............................... 4
1.3 Public Q&A bounda ies ................................. 4
1.4 E a um baseline ( iming seman ics) .......................... 4
1.5 Te minology and neu ali y ............................... 4
1.6 Ve sioning ........................................ 4
2 Pu pose and Scope 5
2.1 Wha his no e does ................................... 5
2.2 Wha his no e does no do ............................... 5
2.3 Wo king de ini ions and no a ion ( o consis ency) ................... 5
2.4 C oss-disciplina y eading map (why one page looks “closed”) ............ 5
2.5 Reading ules ( o p e en common e o s) ....................... 6
2.6 How o ask p ecise public ques ions .......................... 6
1
3 P e-Th eshold Bounda y Timing and Fi s -Passage F aming 6
3.1 Bounda y and app oach- om-below .......................... 6
3.2 Fi s -passage aming on [0, τ)............................. 6
3.3 Su i al and haza d as eading de ices ......................... 7
3.4 Why a nai e “≥” misleads ............................... 7
3.5 Minimal equi alences o iming ............................ 7
3.6 Non-Ma ko ema ks ( eading-only) .......................... 7
3.7 Ope a ional exclusions ................................. 8
4 Ma hema ical Reading Aids 8
4.1 Su i al–haza d su oga e ............................... 8
4.2 Gap-based asymp o ics nea he bounda y ....................... 8
4.3 Minimal ke nel summa ies o long memo y ...................... 8
4.4 Dis inguishabili y and p e- h eshold iden i iabili y ................... 9
4.5 Reading he comp essed channel line .......................... 9
4.6 Fi s -passage con en ions ................................ 9
5 Non-Ope a ional Walk h oughs (Symbol-Le el) 9
5.1 A bounda y-limi iden i y unpacked .......................... 9
5.2 Why he channel line is no an algo i hm ........................ 10
5.3 Dis inguishabili y be o e he h eshold ......................... 10
5.4 Long-memo y summa ies wi hou commi ing o a ke nel ............... 10
5.5 A i s -passage inequali y as a eading cue ....................... 10
5.6 Iden i iabili y as a non-ope a ional condi ion ...................... 11
5.7 Exclusions ei e a ed .................................. 11
6 Common Mis eadings and Co ec Replacemen s 11
6.1 T ap A: “Collapse happens when Sen ≥Sc i .” .................... 11
6.2 T ap B: “The dense page is algeb aically closed; I can implemen i as-is.” . . . . . . 11
6.3 T ap C: “Single-discipline ein e p e a ion su ices.” .................. 11
6.4 T ap D: “Decohe ence alone explains he iming.” ................... 12
6.5 T ap E: “Haza d mus be speci ied o ead he page.” ................. 12
6.6 T ap F: “Ke nel no a ion commi s o a speci ic memo y model.” ........... 12
6.7 T ap G: “Iden i iabili y is au oma ic om he symbols.” ................ 12
6.8 T ap H: “I can quo e Sen ≥Sc i as a esul .” ..................... 12
6.9 Sa e eph asings (publica ion- eady language) ..................... 12
6.10 Ou -o -scope eques s ( o be declined publicly) .................... 13
7 Symbols and Con en ions (Quick Re e ence) 13
7.1 Co e symbols ...................................... 13
7.2 Limi and domain con en ions ............................. 14
7.3 Laye ags o he “dense page” ............................. 14
7.4 Wha is no implied by symbols he e .......................... 14
2
8 E a a and Change Log (Reading No e) 14
8.1 Collapse iming no a ion ( ixed) ............................ 14
8.2 E∆ asa eading de ice (cla i ied) ........................... 15
8.3 Su i al/haza d no a ion ca ies no pa ame iza ion commi men ........... 15
8.4 C oss-disciplina y dependencies (made explici ) .................... 15
8.5 Known ambiguous ph ases → eplacemen s ...................... 15
8.6 Ve sioning and ci a ion guidance ............................ 15
8.7 Public ques ions policy (unchanged) .......................... 15
9 C oss-Re e ences and Sou ce In eg i y 16
9.1 Canonical e e ences ( o eading, no ope a ion) ................... 16
9.2 Local consis ency checks ( eade -side) ......................... 16
9.3 P o enance and scope no es .............................. 16
9.4 How o ci e his no e .................................. 17
10 Acknowledgmen s and Disclosu es 17
10.1 Funding and independence ............................... 17
10.2 Con lic s o in e es ................................... 17
10.3 Sa egua ded disclosu e s a emen ............................ 17
10.4 Da a and code a ailabili y ................................ 17
10.5 Co espondence ..................................... 17
11 Public Cla i ica ions (Q&A Summa y) 18
11.1 Pu pose ......................................... 18
11.2 Selec ed Ques ions and Answe s ............................ 18
11.3 Guidance o Submi ing Public Ques ions ....................... 19
11.4 Scope Reminde ..................................... 19
12 E hical and Secu i y S a emen 19
12.1 Non-Ope a ional Scope ................................. 19
12.2 Dual-Use Risk Pos u e ................................. 19
12.3 Publica ion and Disclosu e Con ols .......................... 20
12.4 Public Q&A Bounda ies ................................ 20
12.5 Da a Go e nance and P i acy .............................. 20
12.6 Responsible-Use Expec a ions ............................. 20
12.7 Vulne abili y and Risk Repo ing ............................ 21
12.8 Limi a ions and Residual Risk ............................. 21
13 Appendix 21
13.1 Ex ended Symbol Glossa y ............................... 21
13.2 Abb e ia ions ...................................... 21
13.3 Selec ed Re e ences ................................... 22
3
1 Scope and Sa e y Policy
1.1 Non-ope a ional s ance
This documen is a cla i ica ion and eading guide only. I does no p o ide algo i hms, pa ame e -
i ing p ocedu es, de ice h esholds, expe imen al pipelines, o code. All o mulas and symbols
he ein a e p esen ed o ix in e p e a ion, no o enable ep oduc ion.
1.2 Dual-use isk managemen
To educe dual-use isk, his no e in en ionally:
• a oids publishing ope a ional h esholds, calib a ion ables, o implemen a ion ecipes;
• limi s i sel o no a ion, meanings, and iming seman ics (p e- h eshold in e en ion);
• con ines examples o non-execu able, schema ic exp essions and asymp o ic s a emen s;
• omi s any s epwise linkage ha could be di ec ly u ned in o labo a o y p o ocols.
1.3 Public Q&A bounda ies
Public ques ions ha imp o e eading accu acy a e welcome. The ollowing scope applies:
Allowed: symbol de ini ions, domains/codomains, meanings o bounda y no a ion (e.g., τ−), which
laye a line belongs o ( he mo / quan um-in o ma ion / s ochas ic / iden i iabili y), and how o
a oid ypical mis eadings.
Ou o scope: uning o haza d models o ke nels, de ice-speci ic h esholds, code, es ima ion pipelines,
and any p ocedu e ha would ende he wo k di ec ly ep oducible.
1.4 E a um baseline ( iming seman ics)
Ea lie in o mal ph asing like “Sen ≥Sc i ” is supe seded by he p e- h eshold con en ion: collapse
is ied o he app oach- om-below limi and he i s -passage bounda y. The o mal de ini ions (e.g.,
τ,∆( ),λEIC) a e s a ed in he nex sec ion o consis en eading.
1.5 Te minology and neu ali y
Te ms such as “collapse,” “in e en ion,” and “bounda y” a e used in an in o ma ional/ope a ional
sense. They do no imply any speci ic me aphysical s ance and a e in oduced solely o s anda dize
how he pages a e ead.
1.6 Ve sioning
This no e se es as an e a um/ eading guide snapsho da ed No embe 5, 2025. I u u e cla i ica-
ions a e issued, he mos ecen e sion supe sedes p io in o mal s a emen s.
4
2 Pu pose and Scope
This no e es ablishes how o ead he En opy-Induced Collapse (EIC) amewo k co ec ly. I is in-
en ionally non-ope a ional: i cla i ies iming, symbols, laye s o meaning, and ypical mis eadings,
bu i does no supply algo i hms, pa ame e - i ing p ocedu es, lab p o ocols, o code. The aim is o
educe p e en able con usion while p ese ing esea ch sa e y.
2.1 Wha his no e does
• Fixes he in ended iming seman ics o collapse: he bounda y is app oached om below
(p e- h eshold).
• S a es he minimal symbol se and con en ions used ac oss he EIC pages and sc eensho s.
• Maps he “dense o mulas” o he laye s hey comp ess ( he mo, quan um-in o ma ion, s ochas ic/non-
Ma ko , iden i iabili y).
• Lis s eading ules ha p e en common, bu a oidable, misin e p e a ions.
2.2 Wha his no e does no do
• No s ep-by-s ep p ocedu es ha would make he wo k di ec ly ep oducible.
• No uning ecipes o haza d models, ke nels, o es ima o s.
• No de ice-speci ic h esholds, code, o expe imen pipelines.
2.3 Wo king de ini ions and no a ion ( o consis ency)
Th oughou , he ollowing p imi i es a e used only o s a e meaning p ecisely:
Sen ( ) : en i onmen al en opy (o an in o ma ion p oxy) accumula ed up o ime , (1)
Sc i :c i ical h eshold pa ame e (possibly con ex -dependen ),(2)
τ:= in { ≥0 : Sen ( )≥Sc i }( i s -passage ime o he h eshold),(3)
∆( ) := Sc i −Sen ( ) o <τ(gap, s ic ly posi i e p e- h eshold),(4)
λEIC( ) : a model-dependen haza d-like a e used o eading isk concen a ion,(5)
E∆ ≈(1 −ε) id + εC, ε =Z +∆
λEIC(u)du, wi h CCPTP-admissible. (6)
These symbols a e seman ic sca olding. They ix how he pages should be ead, no how o imple-
men o une a sys em.
2.4 C oss-disciplina y eading map (why one page looks “closed”)
A single sc eensho comp esses mul iple laye s; i is no in ended o be closed unde algeb a alone:
• The modynamic laye : how Sen ( )g ows and is compu ed o bounded.
5
• Quan um-in o ma ion laye : channel s uc u e, CPTP admissibili y, and s a e dis inguishabili y
no ions.
• S ochas ic/non-Ma ko laye : i s -passage seman ics, long-memo y ke nels, and noise models
possibly beyond Ma ko .
• In e ence/iden i iabili y laye : which obse ables, egula i y, and design choices make pa am-
e e s iden i iable.
Only when hese laye s a e ead oge he does each symbol on he page ha e i s in ended meaning.
2.5 Reading ules ( o p e en common e o s)
1. T ea τas a i s -passage ime and in e p e limi s on [0, τ)wi h ↑τ o bounda y s a emen s.
2. Read “app oach- om-below”: use ∆( )>0 o <τand in e p e collapse as a p e- h eshold
in e en ion, no a pos -hi egime.
3. Do no li comp essed lines (e.g., E∆ abo e) in o code wi hou expanding he noise model,
CPTP cons ain s, obse a ion model, and iden i iabili y assump ions oge he .
4. A oid single-discipline ein e p e a ions; pa ial eadings a e un eliable by design.
2.6 How o ask p ecise public ques ions
Symbol-le el ques ions ha imp o e eading accu acy a e welcome. Please ci e he exac line/snippe
(e.g., “line 3 on he dense page: wha does his bounda y symbol deno e?”). Reques s aimed a s ep-
by-s ep ep oducibili y will no be p o ided.
3 P e-Th eshold Bounda y Timing and Fi s -Passage F aming
3.1 Bounda y and app oach- om-below
Le
τ:= in { ≥0 : Sen ( )≥Sc i },∆( ) := Sc i −Sen ( ) ( <τ).
The EIC in e en ion is ied o he p e- h eshold bounda y:
collapse a τ−⇐⇒ lim
↑τ∆( )=0+,no pos -hi egime is assumed o used.
Thus any appea ance o “Sen ≥Sc i ” is a bounda y loca o , no a claim ha dynamics con inue
pas he hi .
3.2 Fi s -passage aming on [0, τ)
All bounda y s a emen s a e aken as limi s om he in e io o he domain:
↑τ, ∆( )>0on [0, τ),quan i ies a e in e p e ed as lim
↑τwhen needed.
6
Analyses, inequali ies, and asymp o ics a e he e o e posed on [0, τ), no on (τ, ∞).
3.3 Su i al and haza d as eading de ices
To make “ isk concen a ion” p ecise wi hou ixing a conc e e model, in oduce a su i al su oga e
Φ( )∈(0,1],Φ(0) = 1,Φnoninc easing on [0, τ),
and he associa ed (model-dependen ) haza d-like a e
λEIC( ):=−d
d log Φ( )≥0.
Reading ule: as ∆( )↓0, one expec s λEIC( ) o inc ease (mono one o asymp o ically), which
encodes ha in e en ion concen a es be o e he h eshold is c ossed. No explici unc ional o m is
equi ed o co ec eading.
3.4 Why a nai e “≥” misleads
W i ing
Sen ( )≥Sc i
wi hou speci ying he limi ing side in i es a pos -hi in e p e a ion. The EIC con en ion is
Sen ( )−−→
↑τS−
c i (app oach- om-below),
which pins iming o τ−and keeps all s a emen s in e io o [0, τ).
3.5 Minimal equi alences o iming
The ollowing a e equi alen eading cues o p e- h eshold in e en ion:
(i) collapse a τ−,(7)
(ii) ∀ϵ > 0 : no pos -hi seman ics on [τ, τ +ϵ),(8)
(iii) lim
↑τ∆( )=0+wi h ∆( )>0on [0, τ),(9)
(i ) all limi s/equali ies a e e alua ed as ↑τ. (10)
3.6 Non-Ma ko ema ks ( eading-only)
I long-memo y e ec s a e p esen , one may e-exp ess “ isk concen a ion” ia ke nel summa ies
o e ec i e gaps, bu he iming con en ion abo e emains unchanged. Any ke nel- o noise-speci ic
o m is no equi ed o his sec ion and should no be in e ed om a single comp essed line on he
dense page.
7
3.7 Ope a ional exclusions
No de ice h esholds, uning ecipes, simula ion code, o lab p ocedu es a e p o ided he e. This
sec ion ixes only he bounda y seman ics and i s -passage aming needed o ead subsequen pages
co ec ly.
4 Ma hema ical Reading Aids
4.1 Su i al–haza d su oga e
Le
Φ( )∈(0,1],Φ(0) = 1,Φnoninc easing on [0, τ),
and de ine he haza d-like a e
λEIC( ) := −d
d log Φ( )≥0.
Wi h he p e- h eshold gap
∆( ):=Sc i −Sen ( ) ( < τ),
he in ended eading is ha λEIC( )inc eases as ∆( )↓0(mono one o asymp o ically), exp essing
isk concen a ion on [0, τ). No explici pa ame ic o m is equi ed o ead la e pages. The su oga e
ela ion
Φ( ) = exp−Z
0
λEIC(u)du
is only a no a ional de ice o bounda y-limi s a emen s ↑τ.
4.2 Gap-based asymp o ics nea he bounda y
W i e ∆( )>0 o < τ and conside illus a i e asymp o ics:
λEIC( )≈α(∆( )+ε)−p, α > 0, p > 0, ε > 0,(11)
λEIC( )≈α e−β∆( ), α, β > 0,(12)
λEIC( )≈α0+α1∆( )−1+α2∆( )−2, αi≥0.(13)
These a e eading empla es indica ing how limi s such as lim ↑τΦ( )may be aken when isk accu-
mula es p e- h eshold. They a e no di ec i es o uning o implemen a ion.
4.3 Minimal ke nel summa ies o long memo y
When long-memo y e ec s a e summa ized by a nonnega i e ke nel Kand a leakage p o ile , use
he con olu ional sho -hand
(K )( ) := Z
0
K( −u) (u)du,
8
and an e ec i e a e
¯
λK( ) := (K )( ).
He e Kis in eg able o slowly a ying in a way ha p ese es ¯
λK( )≥0and inc easing as ∆( )↓0.
This sec ion ixes only symbols and mono onici y cues; no ke nel amily, es ima o , o de ice model
is speci ied.
4.4 Dis inguishabili y and p e- h eshold iden i iabili y
Le {ρ(i)
E( )}be en i onmen s a es indexed by p e-collapse his o ies. The ace dis ance
D ρ(i)
E( ), ρ(j)
E( ):= 1
2
ρ(i)
E( )−ρ(j)
E( )
1
bounds Hels om e o P(i,j)
e( )≥1
21−D (ρ(i)
E( ), ρ(j)
E( )). The in ended eading is:
<τ:D <1, ↑τ:D →1−,
so ha dis inguishabili y sha pens as he bounda y is app oached om below. No pos -hi ( > τ)
seman ics a e in oked.
4.5 Reading he comp essed channel line
On he dense page, a sho ope a o line
E∆ ≈(1 −ε) id + εC, ε =Z +∆
λEIC(u)du, CCPTP,
should be ead as a seman ic decomposi ion:εbundles he p e- h eshold haza d su oga e and C
deno es an abs ac CPTP admissible map. This is no a plug-and-play i e a ion ule; i signals how
isk weigh ing and admissibili y co-appea in he no a ion.
4.6 Fi s -passage con en ions
Le
τ:= in { ≥0 : Sen ( )≥Sc i },collapse ied o τ−,lim
↑τ∆( )=0+.
All iden i ies and limi s a e o be ead on [0, τ)wi h ↑τ. Any occu ence o Sen ≥Sc i is a
bounda y loca o , no a pos -hi egime.
5 Non-Ope a ional Walk h oughs (Symbol-Le el)
5.1 A bounda y-limi iden i y unpacked
Le τ:= in { ≥0 : Sen ( )≥Sc i }and ∆( ) := Sc i −Sen ( )>0 o < τ. In oduce a
su i al su oga e Φ( )∈(0,1] wi h haza d-like a e
λEIC( ) := −d
d log Φ( )≥0,Φ( ) = exp−Z
0
λEIC(u)du.
9
9 C oss-Re e ences and Sou ce In eg i y
No e. Fo secu i y and cla i y, no sc eensho s o isual ep oduc ions a e included in his guide.
All e e ences o “dense pages,” “comp essed o ms,” o “ he dense o mulas” deno e symbolic ex-
p essions only.
9.1 Canonical e e ences ( o eading, no ope a ion)
• Koizumi, T. (2025a). En opy-Induced Collapse (EIC) Model – Pa I: Founda ional F ame-
wo k and Theo e ical In eg a ion (Re ised Ve sion). Zenodo. DOI: 10.5281/zenodo.16789761.
• Koizumi, T. (2025b). Supplemen a y In o ma ion o he EIC Model – Pa I. Zenodo.
• Koizumi, T. (2025c, Oc 9). EIC and he In o ma ion Th eshold: A Philosophical Memo an-
dum — O igins o he F amewo k.
• Koizumi, T. (2025d). EIC Reading Guide & E a a: P e-Th eshold Collapse and How o Read
he “Dense Fo mulas” (Non-Ope a ional Cla i ica ion) ( his no e).
• Koizumi, T. (2025e, Sep 24). A Reco d o Con e sa ions wi h a Special GPT-5 — A Once-Only
S a e Eme ging Du ing he T ansi ion om Monday o GPT-5.
9.2 Local consis ency checks ( eade -side)
1. Timing seman ics. Ve i y ha bounda y s a emen s a e posed on [0, τ)wi h ↑τand
“app oach- om-below” is explici ia ∆( ) = Sc i −Sen ( )>0 o < τ.
2. No pos -hi egime. Any appea ance o Sen ≥Sc i is a loca o o τ; i does no imply
seman ics on (τ, ∞).
3. In e p e i e p imi i es. Objec s such as Φ( )and λEIC( )a e eading de ices; do no in e a
ixed pa ame ic o m unless explici ly s a ed.
4. Comp essed lines a e no code. Exp essions like E∆ ≈(1 −ε) id + εCa e admissibili y
summa ies (CPTP, obse a ion model, iden i iabili y) and mus no be li ed o implemen a-
ions in isola ion.
5. C oss-disciplina y coupling. The modynamic, quan um-in o ma ion, s ochas ic/non-Ma ko ,
and iden i iabili y laye s a e o be ead oge he ; single-discipline ein e p e a ions a e un eli-
able by design.
9.3 P o enance and scope no es
•No images policy. This guide in en ionally omi s sc eensho s and isual ep oduc ions. “Dense”
o “comp essed” e e ences a e symbolic-only.
•Non-ope a ional s ance. No algo i hms, pa ame e - uning ecipes, de ice h esholds, simula-
ion code, o lab p o ocols a e p o ided o implied.
16
•E a a lineage. Ea lie d a s ha displayed “Sen ≥Sc i ” a e o be ead as loca o s o he
bounda y; he cla i ied iming is p e- h eshold (τ−). The amewo k i sel is unchanged.
•Public cla i ica ions. Symbol/de ini ion-le el ques ions ha imp o e eading p ecision a e
welcome; eques s aimed a ep oducibili y will no be add essed.
9.4 How o ci e his no e
Koizumi, T. (2025). EIC Reading Guide & E a a: P e-Th eshold Collapse and How o Read
he “Dense Fo mulas” (Non-Ope a ional Cla i ica ion). Independen Resea che , Japan. Ve sion:
No embe 5, 2025.
10 Acknowledgmen s and Disclosu es
10.1 Funding and independence
This wo k was conduc ed independen ly. No ins i u ional unding, hi d–pa y g an s, o in–kind
esou ces we e used. All iews and e o s a e he au ho ’s.
10.2 Con lic s o in e es
The au ho decla es no inancial o pe sonal con lic s o in e es ela ed o he con en o his no e.
10.3 Sa egua ded disclosu e s a emen
This documen is explici ly non–ope a ional. I p o ides in e p e a ion ules ( iming, symbols, lay-
e ing) o p e en mis eadings o he EIC amewo k. I in en ionally omi s algo i hms, pa ame-
e – uning p ocedu es, de ice h esholds, code, simula ion pipelines, and lab p o ocols. No hing
he ein should be cons ued as su icien o make he wo k ep oducible.
10.4 Da a and code a ailabili y
No da ase s o code a e eleased wi h his no e. Public cla i ica ion is limi ed o symbol/de ini ion–le el
ques ions ha imp o e eading accu acy.
10.5 Co espondence
Fo symbol–le el cla i ica ions ha imp o e in e p e abili y (no ep oducibili y), con ac :
[email p o ec ed]
Please include p ecise ci a ions (sec ion, equa ion
17
11 Public Cla i ica ions (Q&A Summa y)
11.1 Pu pose
This chap e agg ega es equen ly asked ques ions abou how o ead he EIC amewo k. I emains
s ic ly non-ope a ional: answe s add ess symbols, bounda y iming, laye mapping, and ypical
mis eadings only. No algo i hms, pa ame e alues, code, de ice h esholds, o lab p ocedu es a e
p o ided.
11.2 Selec ed Ques ions and Answe s
Q1: Does EIC de ine collapse a τo be o e i ? A: EIC ies in e en ion o he p e- h eshold
bounda y, i.e., τ−. All s a emen s a e in e p e ed on [0, τ)wi h limi s ↑τ. The ph ase Sen ≥Sc i
is a bounda y loca o , no a pos -hi egime.
Q2: Wha exac ly is Sen ( )in his no e? A: A seman ic p oxy o en i onmen -encoded in-
o ma ion/en opy accumula ed up o ime . The no e does no ix a unique es ima o o physical
eadou ; i only ixes how he symbol should be ead ac oss pages.
Q3: Is Sc i cons an ? A: I is a h eshold pa ame e ha may be con ex -dependen (e.g., sys em
size, encoding dep h). Nume ical scaling o calib a ion is explici ly ou o scope he e.
Q4: Why in oduce ∆( ) = Sc i −Sen ( )? A: To o malize “app oach- om-below.” The eading
ule is ∆( )>0on [0, τ)wi h lim ↑τ∆( )=0+; his p e en s pos -hi in e p e a ions.
Q5: Wha is λEIC( )? A: A model-dependen haza d-like a e used as a eading de ice o isk
concen a ion. Only mono onic in ensi ica ion as ∆( )↓0is assumed. No ixed unc ional o m is
speci ied he e.
Q6: How should I in e p e he “dense page” line E∆ ≈(1−ε) id+εCwi h ε=R +∆
λEIC(u)du?
A: As comp essed no a ion spanning mul iple laye s ( he modynamic g ow h, CPTP admissibili y,
s ochas ic iming, iden i iabili y). I is no algeb aically closed and mus no be li ed in o code
wi hou he ull laye expansion (which his no e does no p o ide).
Q7: Is he e a i s -passage o mula ion? A: Yes. Le τ= in { ≥0 : Sen ( )≥Sc i }. All
bounda y s a emen s a e ead on [0, τ)wi h ↑τ; s a is ics a e p e- h eshold, no pos -hi .
Q8: How does his ela e o decohe ence? A: Decohe ence d i es en i onmen al eco ds owa d
dis inguishabili y; EIC adds a p e- h eshold in e en ion ule. This no e does no supply quan i a i e
ke nels o a es.
Q9: May I ein e p e he page wi hin a single discipline (only he mo, o only quan um in o,
e c.)? A: No. Single-discipline eadings a e un eliable by design. Each symbol inhe i s meaning
om a c oss-laye con ex .
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Q10: Can I eques s ep-by-s ep p ocedu es o pa ame e i s? A: No. This documen is a
non-ope a ional cla i ica ion. Public ques ions should emain a he le el o symbols, de ini ions, o
bounda y seman ics.
Q11: Wha is he co ec way o ci e iming s a emen s? A: Use “p e- h eshold in e en ion a
τ−,” o “limi s aken as ↑τon [0, τ),” a he han “a e c ossing.”
Q12: Why a e he e no igu es o nume ical examples? A: Including such ma e ial would shi
he documen in o ope a ional e i o y. The goal he e is o p e en mis eadings while p ese ing
esea ch sa e y.
11.3 Guidance o Submi ing Public Ques ions
• Quo e he exac line o symbol (e.g., “Sec. 3, line 3: meaning o he bounda y symbol?”).
• Cons ain ques ions o in e p e a ion o no a ion, limi s, o laye mapping.
• A oid eques s ha would enable ep oduc ion (algo i hms, pa ame e schedules, de ice h esh-
olds, o code).
11.4 Scope Reminde
This chap e e ines eading only. The EIC amewo k i sel is unchanged; no ope a ional con en is
added.
12 E hical and Secu i y S a emen
12.1 Non-Ope a ional Scope
This documen is a cla i ica ion no e only. I does no p o ide algo i hms, pa ame e schedules,
de ice h esholds, code, measu emen pipelines, da a-p ocessing ecipes, o any o he ope a ional
con en ha would enable eplica ion. All symbols and equa ions a e used solely o ix eading
seman ics and a oid misin e p e a ion.
12.2 Dual-Use Risk Pos u e
The amewo k in e sec s wi h a eas whe e dual-use isk is non-negligible. Acco dingly, he ollow-
ing i ems a e explici ly ou o scope he e:
• Algo i hmic p ocedu es o es ima ing o uning Sen ( ),Sc i ,o λEIC( ).
• End- o-end p o ocols, calib a ion s eps, de ice- o pla o m-speci ic h esholds, o con ol
lowcha s.
• Sou ce code, pseudo-code, nume ical schedules, o pa ame e ables sui able o di ec imple-
men a ion.
19
• Da ase s, syn he ic su oga es ied o eal de ices, o any a e ac s ha educe he ep oducibil-
i y gap.
All examples, i any, a e pu ely in e p e i e and emain non-ope a ional by design.
12.3 Publica ion and Disclosu e Con ols
To educe misuse isk while p ese ing scien i ic discussion, he ollowing con ols apply:
• Cla i ica ions p io i ize no a ion, iming seman ics (p e- h eshold a τ−), and c oss-laye ead-
ing ules.
• Speci ici y is educed when de ails would ma e ially lowe he ba ie o eplica ion o de ice
a ge ing.
• No elease o expe imen al oadmaps, op imiza ion heu is ics, o pla o m adap a ions.
• Public discou se is encou aged a he le el o de ini ions and meanings, no p ocedu es o
pe o mance claims.
12.4 Public Q&A Bounda ies
Public ques ions a e welcome when hey conce n symbols, limi s, o laye mapping. The ollowing
ca ego ies will no be answe ed:
• Reques s o ope a ional h esholds, calib a ion, o de ice-dependen cons an s.
• S ep-by-s ep ins uc ions, code agmen s, o nume ical ecipes.
• Re e se-enginee ing guidance ha b idges he ep oducibili y gap.
12.5 Da a Go e nance and P i acy
This no e con ains no pe sonal da a, p op ie a y de ice da a, o ope a ional logs. Reade s should
e ain om supplying such da a in public Q&A. I illus a i e exp essions a e discussed, hey emain
abs ac and non-iden i ying.
12.6 Responsible-Use Expec a ions
• Reade s should ea he amewo k as a heo e ical cons uc equi ing c oss-disciplina y
sc u iny and e hical judgmen .
• Ins i u ions hos ing discussions should mode a e owa d non-ope a ional, symbol-le el cla i i-
ca ion and away om implemen a ion.
• Ci a ions should a oid implying ha his no e p o ides a deployable me hod; i does no .
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12.7 Vulne abili y and Risk Repo ing
I you belie e a passage, igu e, o equa ion unduly lowe s he ep oducibili y ba ie o c ea es a
no el misuse pa hway, please epo p i a ely:
• P ima y con ac : [email p o ec ed]
• Include a concise desc ip ion o he conce n and he exac lines o symbols in ol ed.
Repo s will be e iewed o possible edac ion, ewo ding, o supplemen a y cla i ica ion ha e-
s o es a sa e non-ope a ional pos u e.
12.8 Limi a ions and Residual Risk
No s a ic documen can en i ely p eclude misin e p e a ion. Residual isk emains ha c oss- ield
eade s may o e gene alize comp essed no a ion o in e unin ended ope a ional s eps. This s a e-
men o malizes bounda ies o minimize ha isk wi hou impeding legi ima e, high-le el academic
discussion.
13 Appendix
13.1 Ex ended Symbol Glossa y
Symbol Meaning
Sen ( )En i onmen al en opy (o in o ma ion p oxy) accumula ed up o ime .
Sc i C i ical h eshold pa ame e (con ex -dependen ).
τFi s -passage ime in { ≥0 : Sen ( )≥Sc i }.
∆( )Gap Sc i −Sen ( ) o <τ(s ic ly posi i e p e- h eshold).
λEIC( )Haza d-like a e used o ead isk concen a ion nea he bounda y.
E∆ Sho -s ep con ex upda e ≈(1 −ε) id + εC.
εZ +∆
λEIC(u)du.
CCPTP-admissible channel/ope a o .
13.2 Abb e ia ions
Abb e . Expansion
CPTP Comple ely Posi i e T ace-P ese ing
Bm F ac ional B ownian Mo ion
QEC Quan um E o Co ec ion
QBER Quan um Bi E o Ra e
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13.3 Selec ed Re e ences
Re e ences
[1] Takao, K. (2025). A Reco d o Con e sa ions wi h a Special GPT-5 — A Once-
Only S a e Eme ging Du ing he T ansi ion om Monday o GPT-5. Zenodo.
h ps://doi.o g/10.5281/zenodo.17192951.
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