Pith Number

pith:B63MFACP

pith:2010:B63MFACP2R3A5BL554MDHQYXQS

not attested not anchored not stored refs pending

Very ample polarized self maps extend to projective space

Anupam Bhatnagar, Lucien Szpiro

arxiv:1010.2715 v2 · 2010-10-13 · math.DS · 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{B63MFACP2R3A5BL554MDHQYXQS}

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	2026-05-18T04:06:55.125900Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fb6c2804fd4760e857def1833c31784841a8f5d1d6a9b6eb84006b71e6f3938

Aliases

arxiv: 1010.2715 · arxiv_version: 1010.2715v2 · doi: 10.48550/arxiv.1010.2715 · pith_short_12: B63MFACP2R3A · pith_short_16: B63MFACP2R3A5BL5 · pith_short_8: B63MFACP

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/B63MFACP2R3A5BL554MDHQYXQS \
  | 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: 0fb6c2804fd4760e857def1833c31784841a8f5d1d6a9b6eb84006b71e6f3938

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "960a4668ed9839444f8910717c8937f24a8c6e178d0802b62440b9d7428c9ca0",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2010-10-13T18:01:15Z",
    "title_canon_sha256": "1756b5ccf9d1489bcf7383bf9f450ffccc90935f91aec2fb07146b56277a69a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2715",
    "kind": "arxiv",
    "version": 2
  }
}