Pith Number

pith:TV4MGPJX

pith:2021:TV4MGPJXGAPP45FUM5Q6BXIBPL

not attested not anchored not stored refs pending

Morse theory for loop-free categories

David Mosquera-Lois, Mateusz Przybylski, Micha{\l} Lipi\'nski

arxiv:2107.06202 v2 · 2021-07-13 · 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{TV4MGPJXGAPP45FUM5Q6BXIBPL}

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	2026-06-19T16:12:43.515196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d78c33d37301efe74b46761e0dd017ac438dd43a177049672afbb727ab1214c

Aliases

arxiv: 2107.06202 · arxiv_version: 2107.06202v2 · doi: 10.48550/arxiv.2107.06202 · pith_short_12: TV4MGPJXGAPP · pith_short_16: TV4MGPJXGAPP45FU · pith_short_8: TV4MGPJX

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/TV4MGPJXGAPP45FUM5Q6BXIBPL \
  | 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: 9d78c33d37301efe74b46761e0dd017ac438dd43a177049672afbb727ab1214c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "46deac281ff38d69916ded5ee95d66a39d82eccfcdd3fafbbef7ef61a3718d2f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2021-07-13T16:01:49Z",
    "title_canon_sha256": "47242dfe5ce2c57664b45340b85e43617e76ef4ebc771a242044bc1135a42d49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2107.06202",
    "kind": "arxiv",
    "version": 2
  }
}