Pith Number

pith:QZDDFAI3

pith:2015:QZDDFAI3Y3OEN4ROCYEL7NVXZY

not attested not anchored not stored refs pending

Representation schemes and rigid maximal Cohen-Macaulay modules

Hailong Dao, Ian Shipman

arxiv:1507.06042 v2 · 2015-07-22 · math.AC · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QZDDFAI3Y3OEN4ROCYEL7NVXZY}

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	2026-05-18T01:32:43.369621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

864632811bc6dc46f22e1608bfb6b7ce08bca0989baee8e8cf34b84a9d67dce4

Aliases

arxiv: 1507.06042 · arxiv_version: 1507.06042v2 · doi: 10.48550/arxiv.1507.06042 · pith_short_12: QZDDFAI3Y3OE · pith_short_16: QZDDFAI3Y3OEN4RO · pith_short_8: QZDDFAI3

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/QZDDFAI3Y3OEN4ROCYEL7NVXZY \
  | 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: 864632811bc6dc46f22e1608bfb6b7ce08bca0989baee8e8cf34b84a9d67dce4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9bb5af091224d739ee12d5278dc28c2a63b2334ecad60a86c3dc78e20f3b515f",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-07-22T03:08:43Z",
    "title_canon_sha256": "726dd184f3d751cebaf6a88c2b096ff568baadd3b35b2d884d2c0754bfdd42fb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.06042",
    "kind": "arxiv",
    "version": 2
  }
}