Pith Number

pith:T4SJZRXU

pith:2013:T4SJZRXU2RR2JDPRAKJNYPXASY

not attested not anchored not stored refs pending

Discrete Morse theory for computing cellular sheaf cohomology

Justin Curry, Robert Ghrist, Vidit Nanda

arxiv:1312.6454 v2 · 2013-12-23 · 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{T4SJZRXU2RR2JDPRAKJNYPXASY}

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	2026-05-18T02:19:25.741001Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f249cc6f4d463a48df10292dc3ee0962fc6ee32966abfa147e521861b3bf4d6

Aliases

arxiv: 1312.6454 · arxiv_version: 1312.6454v2 · doi: 10.48550/arxiv.1312.6454 · pith_short_12: T4SJZRXU2RR2 · pith_short_16: T4SJZRXU2RR2JDPR · pith_short_8: T4SJZRXU

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/T4SJZRXU2RR2JDPRAKJNYPXASY \
  | 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: 9f249cc6f4d463a48df10292dc3ee0962fc6ee32966abfa147e521861b3bf4d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "835d7e8f4b94cb7443520c87dac229f38cf4634a2567baf3ee17afd0facd5399",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2013-12-23T02:14:58Z",
    "title_canon_sha256": "3aa2aea0aa55eab2359cdb901681af19749aee0bf1ba279ebb41ac3d9b7cb172"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.6454",
    "kind": "arxiv",
    "version": 2
  }
}