Pith Number

pith:KIUW547T

pith:2002:KIUW547TYEFZGZNIO724Y4JTXB

not attested not anchored not stored refs pending

Multiplication maps of linear systems on smooth projective toric surfaces

Najmuddin Fakhruddin

arxiv:math/0208178 v1 · 2002-08-23 · 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{KIUW547TYEFZGZNIO724Y4JTXB}

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	2026-05-18T01:05:29.416285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52296ef3f3c10b9365a877f5cc7133b87e3eda55443437be17284ec163232ec2

Aliases

arxiv: math/0208178 · arxiv_version: math/0208178v1 · doi: 10.48550/arxiv.math/0208178 · pith_short_12: KIUW547TYEFZ · pith_short_16: KIUW547TYEFZGZNI · pith_short_8: KIUW547T

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/KIUW547TYEFZGZNIO724Y4JTXB \
  | 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: 52296ef3f3c10b9365a877f5cc7133b87e3eda55443437be17284ec163232ec2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bb66e3c9706f4e2977dc4cb7ae72eba06e1407140986f11b83066fcee29bea5",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2002-08-23T08:31:49Z",
    "title_canon_sha256": "569b46661032982d494e38dd781797323ec5718a86d8d1fb2ac4bd9e112a7496"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0208178",
    "kind": "arxiv",
    "version": 1
  }
}