Pith Number

pith:F4ZHOSY5

pith:2021:F4ZHOSY54BDRSQFDB7DO3PXCFL

not attested not anchored not stored refs pending

Multipath cohomology of directed graphs

Carlo Collari, Luigi Caputi, Sabino Di Trani

arxiv:2108.02690 v3 · 2021-08-05 · math.AT · 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{F4ZHOSY54BDRSQFDB7DO3PXCFL}

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	2026-07-05T09:53:37.095212Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f32774b1de0471940a30fc6edbee22ad13b5bf4a18a27542c0f462f42520d19

Aliases

arxiv: 2108.02690 · arxiv_version: 2108.02690v3 · doi: 10.48550/arxiv.2108.02690 · pith_short_12: F4ZHOSY54BDR · pith_short_16: F4ZHOSY54BDRSQFD · pith_short_8: F4ZHOSY5

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/F4ZHOSY54BDRSQFDB7DO3PXCFL \
  | 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: 2f32774b1de0471940a30fc6edbee22ad13b5bf4a18a27542c0f462f42520d19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd396e4e5b3c044305cf2f13d8792a12ad356f18180457a5653a573a10cad847",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2021-08-05T15:50:17Z",
    "title_canon_sha256": "e8f1fbbeb6c386a539b9655a71c3a3a8d468d9337e4812560bf774884b57b679"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.02690",
    "kind": "arxiv",
    "version": 3
  }
}