Pith Number

pith:DZXZ4DNE

pith:2026:DZXZ4DNE272KFEOCLDNSHLFCMQ

not attested not anchored not stored refs pending

The Yang-Mills measure on surfaces via Morse theory

Gabriel Rivi\`ere, Nguyen Viet Dang, Reda Chhaibi, Tat Dat T\^o, Yannick Guedes Bonthonneau

arxiv:2607.24640 v1 · 2026-07-27 · math.PR · math-ph · math.AP · math.DG · math.DS · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DZXZ4DNE272KFEOCLDNSHLFCMQ}

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	2026-07-28T02:24:20.273244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e6f9e0da4d7f4a291c258db23aca2643b0d8f1a927a5d791a2aa344c7a33f1c

Aliases

arxiv: 2607.24640 · arxiv_version: 2607.24640v1 · doi: 10.48550/arxiv.2607.24640 · pith_short_12: DZXZ4DNE272K · pith_short_16: DZXZ4DNE272KFEOC · pith_short_8: DZXZ4DNE

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/DZXZ4DNE272KFEOCLDNSHLFCMQ \
  | 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: 1e6f9e0da4d7f4a291c258db23aca2643b0d8f1a927a5d791a2aa344c7a33f1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "839af26d3f8ae388c2d889f3a3e95475f828b43bfdcf3f6579f50ed46b408d63",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.DG",
      "math.DS",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-27T16:36:59Z",
    "title_canon_sha256": "5dc626ce20b1f6ff90f89a2b57eef1b7b8c72003e3089d32f64dfc898c13f971"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.24640",
    "kind": "arxiv",
    "version": 1
  }
}