Pith Number

pith:CBYOARCL

pith:2013:CBYOARCLGRK7ROYVTJSQX74ZHY

not attested not anchored not stored refs pending

Some applications of Grothendieck Duality Theorem

Chih-Chi Chou

arxiv:1301.0985 v4 · 2013-01-06 · 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{CBYOARCLGRK7ROYVTJSQX74ZHY}

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	2026-05-18T02:47:05.871126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1070e0444b3455f8bb159a650bff993e2b17d9b0d60761ae53288be78e7d8fe2

Aliases

arxiv: 1301.0985 · arxiv_version: 1301.0985v4 · doi: 10.48550/arxiv.1301.0985 · pith_short_12: CBYOARCLGRK7 · pith_short_16: CBYOARCLGRK7ROYV · pith_short_8: CBYOARCL

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/CBYOARCLGRK7ROYVTJSQX74ZHY \
  | 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: 1070e0444b3455f8bb159a650bff993e2b17d9b0d60761ae53288be78e7d8fe2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a07e4f2ab0538ff7b4b074bc7c69ba1129da625191e2b18d7c9c7f61ea624d96",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-01-06T08:15:46Z",
    "title_canon_sha256": "c9903778d7cc7955af44b277cf6fd399736e17617d2a27cc03d792fa7d103720"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.0985",
    "kind": "arxiv",
    "version": 4
  }
}