Pith Number

pith:GHBKY3LA

pith:2013:GHBKY3LAPB7A26QPMI4Q3FRAIG

not attested not anchored not stored refs pending

Sheaves of categories and the notion of 1-affineness

Dennis Gaitsgory

arxiv:1306.4304 v4 · 2013-06-18 · 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{GHBKY3LAPB7A26QPMI4Q3FRAIG}

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	2026-05-18T02:45:32.023269Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31c2ac6d60787e0d7a0f62390d9620419b5d5b3ca1765509dcb9519ad6883036

Aliases

arxiv: 1306.4304 · arxiv_version: 1306.4304v4 · doi: 10.48550/arxiv.1306.4304 · pith_short_12: GHBKY3LAPB7A · pith_short_16: GHBKY3LAPB7A26QP · pith_short_8: GHBKY3LA

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/GHBKY3LAPB7A26QPMI4Q3FRAIG \
  | 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: 31c2ac6d60787e0d7a0f62390d9620419b5d5b3ca1765509dcb9519ad6883036

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c1e16383d13abcc411c8d2495c6259901bf8e3c123eed88a67b3e3fcd55cb62",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-06-18T19:49:05Z",
    "title_canon_sha256": "363b87bad4e7eb55040f29a6cb8701ab732ae512f28c08bcf8d21b6fbbe0ac5c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.4304",
    "kind": "arxiv",
    "version": 4
  }
}