Pith Number

pith:BZSRFB55

pith:2005:BZSRFB555PIZPE6XQTSFBY3C2U

not attested not anchored not stored refs pending

The multiplicity of pairs of modules and hypersurface singularities

Terence Gaffney

arxiv:math/0509045 v1 · 2005-09-02 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BZSRFB555PIZPE6XQTSFBY3C2U}

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	2026-05-18T01:05:23.213223Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e651287bdebd19793d784e450e362d53a828390f75c3f8ad1b37d1ad805bb71

Aliases

arxiv: math/0509045 · arxiv_version: math/0509045v1 · doi: 10.48550/arxiv.math/0509045 · pith_short_12: BZSRFB555PIZ · pith_short_16: BZSRFB555PIZPE6X · pith_short_8: BZSRFB55

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/BZSRFB555PIZPE6XQTSFBY3C2U \
  | 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: 0e651287bdebd19793d784e450e362d53a828390f75c3f8ad1b37d1ad805bb71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dc6677bdcb50e19f8a7ec0d3ab09e962f3eb3f7f378d75bff9aafd2987a9d76",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "",
    "primary_cat": "math.AG",
    "submitted_at": "2005-09-02T15:22:46Z",
    "title_canon_sha256": "cbd6aa1a29c057dbe2ecad247fc0284944838cacf596dd13b8f5757d94cd173f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0509045",
    "kind": "arxiv",
    "version": 1
  }
}