Pith Number

pith:MGUILVUK

pith:2003:MGUILVUKFE7633BZK5VFI2AQBX

not attested not anchored not stored refs pending

Numerical criteria for divisors on $\M_{g}$ to be ample

Angela Gibney

arxiv:math/0312072 v1 · 2003-12-03 · 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{MGUILVUKFE7633BZK5VFI2AQBX}

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	2026-05-17T23:53:12.313513Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61a885d68a293fedec39576a5468100dca6115169bd4757ec59b0abafb2740b3

Aliases

arxiv: math/0312072 · arxiv_version: math/0312072v1 · doi: 10.48550/arxiv.math/0312072 · pith_short_12: MGUILVUKFE76 · pith_short_16: MGUILVUKFE7633BZ · pith_short_8: MGUILVUK

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/MGUILVUKFE7633BZK5VFI2AQBX \
  | 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: 61a885d68a293fedec39576a5468100dca6115169bd4757ec59b0abafb2740b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0347500ad57e3689725b889c6c87cd2b2c232851f421e99a18deed51a308fe5b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2003-12-03T04:11:35Z",
    "title_canon_sha256": "643388ea72a728052bf82e729c49088a4f7c082316763d1a8d3c777786f00b34"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0312072",
    "kind": "arxiv",
    "version": 1
  }
}