Pith Number

pith:TQOUVKDA

pith:2012:TQOUVKDAJM24LAXMWUUGMDS4UT

not attested not anchored not stored refs pending

A nerve lemma for gluing together incoherent discrete Morse functions

Alexander Engstr\"om

arxiv:1209.1290 v2 · 2012-09-06 · math.CO · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TQOUVKDAJM24LAXMWUUGMDS4UT}

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	2026-05-18T03:18:18.587561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c1d4aa8604b35c582ecb528660e5ca4edf8ec9e1e02220b10d3b6f85c4f350a

Aliases

arxiv: 1209.1290 · arxiv_version: 1209.1290v2 · doi: 10.48550/arxiv.1209.1290 · pith_short_12: TQOUVKDAJM24 · pith_short_16: TQOUVKDAJM24LAXM · pith_short_8: TQOUVKDA

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/TQOUVKDAJM24LAXMWUUGMDS4UT \
  | 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: 9c1d4aa8604b35c582ecb528660e5ca4edf8ec9e1e02220b10d3b6f85c4f350a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7af1b446f6f1e743190f897f1eee73851ea2636096cbc9b6e590657899e7c6e",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-06T14:24:10Z",
    "title_canon_sha256": "1286343b54f0cf325a1b57f0a41acc8e82898eace41f128c6a13c2993030c649"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1290",
    "kind": "arxiv",
    "version": 2
  }
}