Pith Number

pith:2ZEAOQB5

pith:2012:2ZEAOQB5AI6I7WRYBL7ALHWBN7

not attested not anchored not stored refs pending

A note on sheaves without self-extensions on the projective $n$-space

Dan Zacharia, Dieter Happel

arxiv:1208.3139 v1 · 2012-08-15 · math.AG · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2ZEAOQB5AI6I7WRYBL7ALHWBN7}

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	2026-05-18T03:48:45.469040Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d64807403d023c8fda380afe059ec16ffdc306b85c1bdddd02288875bfda102f

Aliases

arxiv: 1208.3139 · arxiv_version: 1208.3139v1 · doi: 10.48550/arxiv.1208.3139 · pith_short_12: 2ZEAOQB5AI6I · pith_short_16: 2ZEAOQB5AI6I7WRY · pith_short_8: 2ZEAOQB5

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/2ZEAOQB5AI6I7WRYBL7ALHWBN7 \
  | 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: d64807403d023c8fda380afe059ec16ffdc306b85c1bdddd02288875bfda102f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8de90bbb28a81dc7722787f4a6a877f6d1832728dde483c8661bf87acd21833a",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-08-15T15:23:30Z",
    "title_canon_sha256": "fbeab66ddc24c7861e04ad95f1c285c1a6072474753ef36016dd520d75ff88db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3139",
    "kind": "arxiv",
    "version": 1
  }
}