Pith Number

pith:INVX2EU3

pith:2025:INVX2EU3HECTUP2WLRU5342NSE

not attested not anchored not stored refs pending

Uniqueness of stationary compatible probability measures for chains of infinite order with forbidden transitions

Christophe Gallesco, Daniel Yasumasa Takahashi, Sandro Gallo

arxiv:2507.16981 v2 · 2025-07-22 · math.PR · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{INVX2EU3HECTUP2WLRU5342NSE}

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	2026-05-22T01:03:44.389852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

436b7d129b39053a3f565c69ddf34d9100211691da525e3c6e0826b2df4c094e

Aliases

arxiv: 2507.16981 · arxiv_version: 2507.16981v2 · doi: 10.48550/arxiv.2507.16981 · pith_short_12: INVX2EU3HECT · pith_short_16: INVX2EU3HECTUP2W · pith_short_8: INVX2EU3

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/INVX2EU3HECTUP2WLRU5342NSE \
  | 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: 436b7d129b39053a3f565c69ddf34d9100211691da525e3c6e0826b2df4c094e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab81dc7d7e462aaeacb09b93bd9e8024af5540d6929214f56f5be4e11d061ea8",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-07-22T19:34:40Z",
    "title_canon_sha256": "0099143abaf1737faf42503e0d7fbcb3655392feef1517003e35d3c2c077700e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.16981",
    "kind": "arxiv",
    "version": 2
  }
}