Pith Number

pith:KHLGHVQ6

pith:2025:KHLGHVQ67N7XFZU35KAXGODTXF

not attested not anchored not stored refs resolved

On the entropy of processes generated by quasifactors

R\^omulo M. Vermersch

If a dynamical system has positive entropy, then every full-support quasifactor also has positive entropy.

arxiv:2511.00891 v3 · 2025-11-02 · math.DS

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\usepackage{pith}
\pithnumber{KHLGHVQ67N7XFZU35KAXGODTXF}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

if h_μ(T)>0, then h_μ̃(T̃)>0 for every quasifactor μ̃ of μ having full-support.

C2weakest assumption

The quasifactor μ̃ is required to have full support on the underlying space; without this the entropy positivity may fail.

C3one line summary

Positive entropy of a homeomorphism on a compact metric space is inherited by all full-support quasifactors.

References

32 extracted · 32 resolved · 0 Pith anchors

[1] E. Akin, J. Auslander and A. Nagar,Dynamics of induced systems, Ergodic Theory Dynam. Systems 37(2017), no. 7, 2034–2059 2017

[2] D. V. Anosov,Geodesic flows on closed Riemannian manifolds with negative curvature, Proc. Steklov Inst. Mat. 90 (1967), 1–235 1967

[3] W. Bauer and K. Sigmund,Topological dynamics of transformations induced on the space of proba- bility measures, Monatsh. Math.79(1975), 81–92 1975

[4] N. C. Bernardes Jr., U. B. Darji and R. M. Vermersch,Uniformly positive entropy of induced trans- formations, Ergodic Theory Dynam. Systems42(2022), 9–18 2022

[5] N. C. Bernardes Jr. and R. M. Vermersch,On the dynamics of induced maps on the space of proba- bility measures, Trans. Amer. Math. Soc.368(2016), no. 11, 7703–7725 2016

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-18T03:09:33.608654Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51d663d61efb7f72e69bea81733873b9521f5048f00ca73f5ae48c781347e706

Aliases

arxiv: 2511.00891 · arxiv_version: 2511.00891v3 · doi: 10.48550/arxiv.2511.00891 · pith_short_12: KHLGHVQ67N7X · pith_short_16: KHLGHVQ67N7XFZU3 · pith_short_8: KHLGHVQ6

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KHLGHVQ67N7XFZU35KAXGODTXF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 51d663d61efb7f72e69bea81733873b9521f5048f00ca73f5ae48c781347e706

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab791f47f1f46a3ca31918a242aa69dfdfcf18f6640f01cea18b923b95cfc128",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-11-02T11:22:48Z",
    "title_canon_sha256": "ad80e59284667c84222423e47371b336621ad052db2c32e410acda61d5a0d952"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.00891",
    "kind": "arxiv",
    "version": 3
  }
}