Pith Number

pith:GEXENEND

pith:2019:GEXENENDYRJ7SNQ3I5DDGVXBDK

not attested not anchored not stored refs pending

A sheaf-theoretic approach to tropical homology

Andreas Gross, Farbod Shokrieh

arxiv:1906.09245 v1 · 2019-06-21 · math.AG · math.CO

Open paper page JSON Open Graph Bundle Merged state What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GEXENENDYRJ7SNQ3I5DDGVXBDK}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-17T23:42:44.047539Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

312e4691a3c453f9361b47463356e11a8ab2c95663336b8e20e7fb4624c81a18

Aliases

arxiv: 1906.09245 · arxiv_version: 1906.09245v1 · doi: 10.48550/arxiv.1906.09245 · pith_short_12: GEXENENDYRJ7 · pith_short_16: GEXENENDYRJ7SNQ3 · pith_short_8: GEXENEND

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/GEXENENDYRJ7SNQ3I5DDGVXBDK \
  | 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: 312e4691a3c453f9361b47463356e11a8ab2c95663336b8e20e7fb4624c81a18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "941445d111e0e8f0c2cdcea2656d0de1b0edc16fdf0ad2e21bef4006581b1680",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-06-21T17:10:16Z",
    "title_canon_sha256": "b7798642f24e598c6bfd99e2ac44dd52201c0d16b1bf70971c450e68f428201e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.09245",
    "kind": "arxiv",
    "version": 1
  }
}