Refinement Flow of World-Types: Time as Growth of Stable Distinguishability Paper 41 of the NEMS Suite

{"Paper":[0,120],"36":[1],"showed":[2],"that":[3,31],"stable":[4],"records":[5,52],"force":[6],"an":[7],"arrow":[8],"of":[9,14,47,80],"time":[10],"at":[11,73],"the":[12,37,56,71,74,100,124],"level":[13],"semantics:":[15],"record":[16],"filtration,":[17],"stage":[18],"world-types,":[19],"and":[20,77,85,111],"forgetful":[21],"maps":[22,62],"from":[23],"later":[24],"to":[25],"earlier":[26,75],"stages.":[27],"This":[28],"paper":[29],"reframes":[30],"development":[32,93],"as":[33,51,99],"a":[34,83,87],"refinement":[35],"flow:":[36],"primitive":[38],"evolution":[39],"is":[40,94,127,131],"not":[41],"\\"state":[42],"evolves\\"":[43],"but":[44],"equivalence":[45],"classes":[46],"observational":[48],"indistinguishability":[49],"refine":[50],"accumulate.":[53],"We":[54],"extend":[55,119],"ArrowOfTime":[57],"library":[58,102],"with":[59,70,108],"iterated":[60],"forget":[61],"(\\\\ForgetFromTo_t'":[63],"\\\\to":[64],"t),":[65],"prove":[66],"their":[67],"coherence":[68],"(agreement":[69],"quotient":[72],"stage)":[76],"naturality":[78],"(composition":[79],"forgets":[81],"along":[82],"chain),":[84],"give":[86],"toy":[88,126],"witness":[89],"(two-bit":[90],"world).":[91],"The":[92],"mechanized":[95],"in":[96,103],"Lean":[97],"4":[98],"RefinementFlow":[101],"nems-lean,":[104],"building":[105],"on":[106],"ArrowOfTime,":[107],"zero":[109],"sorry":[110],"no":[112],"custom":[113],"axioms.":[114],"Trust":[115],"boundary.":[116],"Refinement-flow":[117],"lemmas":[118],"36's":[121],"record-filtration":[122],"formalism;":[123],"two-bit":[125],"illustrative":[128],"only.":[129],"Mechanization":[130],"nems-lean":[132],".":[133,135],"See":[134]}

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-13
DOI
https://doi.org/10.5281/zenodo.22733216
Primary Topic
Logic, programming, and type systems
Type
preprint
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
preprint

Refinement Flow of World-Types: Time as Growth of Stable Distinguishability Paper 41 of the NEMS Suite

Nova Spivack
Zenodo (CERN European Organization for Nuclear Research)
Logic, programming, and type systems
preprint

Refinement Flow of World-Types: Time as Growth of Stable Distinguishability Paper 41 of the NEMS Suite

Nova Spivack
preprint en

Abstract

Paper 36 showed that stable records force an arrow of time at the level of semantics: record filtration, stage world-types, and forgetful maps from later to earlier stages. This paper reframes that development as a refinement flow: the primitive evolution is not "state evolves" but equivalence classes of observational indistinguishability refine as records accumulate. We extend the ArrowOfTime library with iterated forget maps (\ForgetFromTo_t' \to t), prove their coherence (agreement with the quotient at the earlier stage) and naturality (composition of forgets along a chain), and give a toy witness (two-bit world). The development is mechanized in Lean 4 as the RefinementFlow library in nems-lean, building on ArrowOfTime, with zero sorry and no custom axioms. Trust boundary. Refinement-flow lemmas extend Paper 36's record-filtration formalism; the two-bit toy is illustrative only. Mechanization is nems-lean . See .

Zenodo (CERN European Organization for Nuclear Research)
Logic, programming, and type systems
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.