Pith Number

pith:WFHKBIMB

pith:2026:WFHKBIMBKDN22QAG4FWHDVXB3T

not attested not anchored not stored refs pending

Natural Invariant Measures for Chaotic Game Dynamics: Finding Order in Chaos

Fryderyk Falniowski, Georgios Piliouras, Jakub Bielawski, Micha{\l} Misiurewicz, Thiparat Chotibut

arxiv:2607.21805 v1 · 2026-07-23 · math.DS · cs.LG · econ.TH

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WFHKBIMBKDN22QAG4FWHDVXB3T}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-07-27T00:20:21.963046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b14ea0a18150dbad4006e16c71d6e1dcdf969ed5b368d926de2f468964546f89

Aliases

arxiv: 2607.21805 · arxiv_version: 2607.21805v1 · doi: 10.48550/arxiv.2607.21805 · pith_short_12: WFHKBIMBKDN2 · pith_short_16: WFHKBIMBKDN22QAG · pith_short_8: WFHKBIMB

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/WFHKBIMBKDN22QAG4FWHDVXB3T \
  | 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: b14ea0a18150dbad4006e16c71d6e1dcdf969ed5b368d926de2f468964546f89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac2e430f6d4e55ef385b0ea19bab429aa7bbab9a9610be2ae7d9146274d9f222",
    "cross_cats_sorted": [
      "cs.LG",
      "econ.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-07-23T20:45:08Z",
    "title_canon_sha256": "2b909e477532c3712fd73c6e648c47d1b07672a15d3b0381c0377d4f31c53248"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21805",
    "kind": "arxiv",
    "version": 1
  }
}