Pith Number

pith:ONSAPSS4

pith:2012:ONSAPSS4ZYVV4UNS5YXBHJAD4E

not attested not anchored not stored refs pending

An arithmetic Hilbert-Samuel theorem for singular hermitian line bundles and cusp forms

Gerard Freixas i Montplet, Robert Berman

arxiv:1209.0996 v1 · 2012-09-05 · math.NT · math.AG · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ONSAPSS4ZYVV4UNS5YXBHJAD4E}

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	2026-05-17T23:53:18.492545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

736407ca5cce2b5e51b2ee2e13a403e1227b7164588918334423956de1fdb4a2

Aliases

arxiv: 1209.0996 · arxiv_version: 1209.0996v1 · doi: 10.48550/arxiv.1209.0996 · pith_short_12: ONSAPSS4ZYVV · pith_short_16: ONSAPSS4ZYVV4UNS · pith_short_8: ONSAPSS4

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/ONSAPSS4ZYVV4UNS5YXBHJAD4E \
  | 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: 736407ca5cce2b5e51b2ee2e13a403e1227b7164588918334423956de1fdb4a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0904af863e32394e28acc1f76de90655d7253532416fca09784a8748ba67aeb",
    "cross_cats_sorted": [
      "math.AG",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-09-05T14:40:35Z",
    "title_canon_sha256": "504656528fff1b61d38e87a55e7648e134907eef24b422fe8cd4f97b8829b9ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.0996",
    "kind": "arxiv",
    "version": 1
  }
}