Pith Number

pith:WQCOTIEI

pith:2015:WQCOTIEIXBKAIOAXLENOFE5EIR

not attested not anchored not stored refs pending

Discrete Morse theory and localization

Vidit Nanda

arxiv:1510.01907 v4 · 2015-10-07 · 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{WQCOTIEIXBKAIOAXLENOFE5EIR}

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	2026-05-18T00:14:23.238442Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b404e9a088b854043817591ae293a4447a8e67451fd1ec7364428c5543624c3e

Aliases

arxiv: 1510.01907 · arxiv_version: 1510.01907v4 · doi: 10.48550/arxiv.1510.01907 · pith_short_12: WQCOTIEIXBKA · pith_short_16: WQCOTIEIXBKAIOAX · pith_short_8: WQCOTIEI

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/WQCOTIEIXBKAIOAXLENOFE5EIR \
  | 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: b404e9a088b854043817591ae293a4447a8e67451fd1ec7364428c5543624c3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cff99af6bc9861297c61ce23d84e782750b42fac22c73cbbac5993838d04828",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2015-10-07T11:52:54Z",
    "title_canon_sha256": "a25bb6ee5048f69eda563db8433281d8144e1f0cd970f754e5d5567507cac95a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.01907",
    "kind": "arxiv",
    "version": 4
  }
}