Pith Number

pith:6KDKVELI

pith:2024:6KDKVELIRSHFW3HHBFN6AQS5L7

not attested not anchored not stored refs pending

Ranks of matrix factorizations and sheaf cohomology

Mark E. Walker, Michael K. Brown

arxiv:2412.01060 v2 · 2024-12-02 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6KDKVELIRSHFW3HHBFN6AQS5L7}

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	2026-07-05T11:54:42.758201Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f286aa91688c8e5b6ce7095be0425d5fe0b2c427506456d086a85d2ef0210cbe

Aliases

arxiv: 2412.01060 · arxiv_version: 2412.01060v2 · doi: 10.48550/arxiv.2412.01060 · pith_short_12: 6KDKVELIRSHF · pith_short_16: 6KDKVELIRSHFW3HH · pith_short_8: 6KDKVELI

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/6KDKVELIRSHFW3HHBFN6AQS5L7 \
  | 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: f286aa91688c8e5b6ce7095be0425d5fe0b2c427506456d086a85d2ef0210cbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1f297d8fd528433d1a1a31c4c3cd20d069b70db754daf9c00d25dd59d6557771",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2024-12-02T02:42:49Z",
    "title_canon_sha256": "4aa4e2b988c267fa55bb7421252769d71bb1c4482eef89af43138e73fbb41c67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.01060",
    "kind": "arxiv",
    "version": 2
  }
}