Pith Number

pith:VRGOQ645

pith:2025:VRGOQ645XHSL25VB2AIOAMY5AF

not attested not anchored not stored refs pending

Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves

Alex Sistko, Cameron Wright, Jaiung Jun

arxiv:2509.08144 v1 · 2025-09-09 · math.CT · math.AG · 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{VRGOQ645XHSL25VB2AIOAMY5AF}

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.

Cited by

1 paper in Pith

On the category of modules over bands: relative schemes, hyperring schemes and proto-exactness

Receipt and verification

First computed	2026-07-05T12:08:23.739621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac4ce87b9db9e4bd76a1d010e0331d015de651d65093d0ef0898fddd00337c0d

Aliases

arxiv: 2509.08144 · arxiv_version: 2509.08144v1 · doi: 10.48550/arxiv.2509.08144 · pith_short_12: VRGOQ645XHSL · pith_short_16: VRGOQ645XHSL25VB · pith_short_8: VRGOQ645

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/VRGOQ645XHSL25VB2AIOAMY5AF \
  | 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: ac4ce87b9db9e4bd76a1d010e0331d015de651d65093d0ef0898fddd00337c0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d78a1ed9cc468167dbb387a0e4096a91b567e0fd62677f542fb1b7a204b894f",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-09-09T20:53:28Z",
    "title_canon_sha256": "52ee3bd0a3944d3f274bb8f4dc2555ea19dabe378c97ab93fe0ae05eab72d189"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.08144",
    "kind": "arxiv",
    "version": 1
  }
}