Pith Number

pith:NX2U74C2

pith:2012:NX2U74C2F5YVNRNAPINB5PMFKW

not attested not anchored not stored refs pending

Smoothing discrete Morse theory

Bruno Benedetti

arxiv:1212.0885 v4 · 2012-12-04 · math.GT · math.CO · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NX2U74C2F5YVNRNAPINB5PMFKW}

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	2026-05-18T02:31:38.526139Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6df54ff05a2f7156c5a07a1a1ebd85559ad979945b550a07606437b88bfca706

Aliases

arxiv: 1212.0885 · arxiv_version: 1212.0885v4 · doi: 10.48550/arxiv.1212.0885 · pith_short_12: NX2U74C2F5YV · pith_short_16: NX2U74C2F5YVNRNA · pith_short_8: NX2U74C2

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/NX2U74C2F5YVNRNAPINB5PMFKW \
  | 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: 6df54ff05a2f7156c5a07a1a1ebd85559ad979945b550a07606437b88bfca706

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3b9ac6d1d41b1cbeb53c9d112373dcb4c86cd4698ba87f18927886d0d68e08a",
    "cross_cats_sorted": [
      "math.CO",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-12-04T21:55:08Z",
    "title_canon_sha256": "8665efde527bd5a91710f082814e0dc0ff758de805801cb1544949b86389ea5d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0885",
    "kind": "arxiv",
    "version": 4
  }
}