Pith Number

pith:4IL2TU6A

pith:2019:4IL2TU6AY6IXJGAKPR3FJ5JJKI

not attested not anchored not stored refs pending

Minimal triangulations of circle bundles, circular permutations and binary Chern cocycle

Nikolai Mn\"ev

arxiv:1908.04029 v2 · 2019-08-12 · math.GT · math.AT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4IL2TU6AY6IXJGAKPR3FJ5JJKI}

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	2026-07-04T23:59:50.761723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e217a9d3c0c79174980a7c7654f529523f263d2e039c5fcace01a7bed37e9267

Aliases

arxiv: 1908.04029 · arxiv_version: 1908.04029v2 · doi: 10.48550/arxiv.1908.04029 · pith_short_12: 4IL2TU6AY6IX · pith_short_16: 4IL2TU6AY6IXJGAK · pith_short_8: 4IL2TU6A

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/4IL2TU6AY6IXJGAKPR3FJ5JJKI \
  | 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: e217a9d3c0c79174980a7c7654f529523f263d2e039c5fcace01a7bed37e9267

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "934403543150a5c9d81cf4e4f9a65116a13ee1251c7f4adee8df18dc2182eac6",
    "cross_cats_sorted": [
      "math.AT",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2019-08-12T07:07:03Z",
    "title_canon_sha256": "d41b4bbc5dfeac22c0b1b51d90ddb05f8e776a72506abb12e752debeb6753d83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.04029",
    "kind": "arxiv",
    "version": 2
  }
}