Pith Number

pith:L72U2RYQ

pith:2010:L72U2RYQ67JAGNLFRAHKXKLVRV

not attested not anchored not stored refs pending

Discrete Morse Theory for Manifolds with Boundary

Bruno Benedetti

arxiv:1007.3175 v2 · 2010-07-19 · math.AT · math.AC · 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{L72U2RYQ67JAGNLFRAHKXKLVRV}

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	2026-05-18T04:39:59.080872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ff54d4710f7d2033565880eaba9758d45301e4c77c0f6e419f3cc192c164ce8

Aliases

arxiv: 1007.3175 · arxiv_version: 1007.3175v2 · doi: 10.48550/arxiv.1007.3175 · pith_short_12: L72U2RYQ67JA · pith_short_16: L72U2RYQ67JAGNLF · pith_short_8: L72U2RYQ

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/L72U2RYQ67JAGNLFRAHKXKLVRV \
  | 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: 5ff54d4710f7d2033565880eaba9758d45301e4c77c0f6e419f3cc192c164ce8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f5a3166e7a7a7e14ba64bc0f0f91d90c1f66817ab7cc51c23cdec6d3ab1b0e5",
    "cross_cats_sorted": [
      "math.AC",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2010-07-19T15:11:46Z",
    "title_canon_sha256": "1a8151c579154fed14ecfcd22fd3b64ddfa258856e049b07ce1fc1a7abc78205"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.3175",
    "kind": "arxiv",
    "version": 2
  }
}