Pith Number

pith:PR67FMZS

pith:2025:PR67FMZSSDKHTAPFT7VUTM4OPD

not attested not anchored not stored refs pending

Non uniform expansion and additive noise imply random horseshoe

Dmitry Turaev, Giuseppe Tenaglia, Jeroen S.W. Lamb

arxiv:2501.11656 v2 · 2025-01-20 · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PR67FMZSSDKHTAPFT7VUTM4OPD}

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	2026-07-05T10:06:47.148968Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c7df2b33290d47981e59feb49b38e78f26fc623862a1651c6529a397135d6fe

Aliases

arxiv: 2501.11656 · arxiv_version: 2501.11656v2 · doi: 10.48550/arxiv.2501.11656 · pith_short_12: PR67FMZSSDKH · pith_short_16: PR67FMZSSDKHTAPF · pith_short_8: PR67FMZS

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/PR67FMZSSDKHTAPFT7VUTM4OPD \
  | 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: 7c7df2b33290d47981e59feb49b38e78f26fc623862a1651c6529a397135d6fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb1a7f8587b4fe277a54ddba84a103f18ed2c46e04e4254bf4f31925878927a5",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2025-01-20T18:39:05Z",
    "title_canon_sha256": "d7bca732b3541345583d774028fe5a3fc8654b0fb3e005e7af08a24996c1b5cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.11656",
    "kind": "arxiv",
    "version": 2
  }
}