Pith Number

pith:QPL4FGZU

pith:2003:QPL4FGZUQOMON57JYTG7FR5QKP

not attested not anchored not stored refs pending

Stability of Arakelov bundles and tensor products without global sections

Norbert Hoffmann

arxiv:math/0304017 v1 · 2003-04-02 · math.NT · 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{QPL4FGZUQOMON57JYTG7FR5QKP}

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	2026-05-18T01:05:28.980063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83d7c29b348398e6f7e9c4cdf2c7b053d7803cfead27dc9b810f3eae6549f8e5

Aliases

arxiv: math/0304017 · arxiv_version: math/0304017v1 · doi: 10.48550/arxiv.math/0304017 · pith_short_12: QPL4FGZUQOMO · pith_short_16: QPL4FGZUQOMON57J · pith_short_8: QPL4FGZU

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/QPL4FGZUQOMON57JYTG7FR5QKP \
  | 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: 83d7c29b348398e6f7e9c4cdf2c7b053d7803cfead27dc9b810f3eae6549f8e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e80242c1ecc327c45a22b9470dedf1212df3647407ae8a126c5803ebe5ea54fb",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2003-04-02T13:01:46Z",
    "title_canon_sha256": "b2a259b9dfc9172077dc39bf58edf40376ca4d60cdb9b4c1135737cc73cba8b8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0304017",
    "kind": "arxiv",
    "version": 1
  }
}