Pith Number

pith:V4OI66CI

pith:2012:V4OI66CIKYVPTO5DZ6FG5MWFLW

not attested not anchored not stored refs pending

The arithmetic Grothendieck-Riemann-Roch theorem for general projective morphisms

Gerard Freixas i Montplet, Jos\'e Ignacio Burgos Gil, Razvan Litcanu

arxiv:1211.1783 v1 · 2012-11-08 · math.AG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V4OI66CIKYVPTO5DZ6FG5MWFLW}

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	2026-05-18T03:41:13.516106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

af1c8f7848562af9bba3cf8a6eb2c55da3293db7291a88b515ad07bad48bf536

Aliases

arxiv: 1211.1783 · arxiv_version: 1211.1783v1 · doi: 10.48550/arxiv.1211.1783 · pith_short_12: V4OI66CIKYVP · pith_short_16: V4OI66CIKYVPTO5D · pith_short_8: V4OI66CI

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/V4OI66CIKYVPTO5DZ6FG5MWFLW \
  | 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: af1c8f7848562af9bba3cf8a6eb2c55da3293db7291a88b515ad07bad48bf536

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "019ed10077b9e4a9929fda74909a4e36494eed7006bb50d86f0bb102422ddcd5",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-11-08T07:59:13Z",
    "title_canon_sha256": "a043561e31d5f9b798b7a5a0c5cbc15bc3c52e1b681122327ef60df8bbc2e9e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.1783",
    "kind": "arxiv",
    "version": 1
  }
}