Pith Number

pith:T54PQWQB

pith:2013:T54PQWQBNDO37H4XQQQQXHPWAD

not attested not anchored not stored refs pending

Singularities with respect to Mather-Jacobian discrepancies

Lawrence Ein, Shihoko Ishii

arxiv:1310.6882 v1 · 2013-10-25 · 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{T54PQWQBNDO37H4XQQQQXHPWAD}

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	2026-05-18T03:08:56.935571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9f78f85a0168ddbf9f9784210b9df600c34895198d075ae98cf0a1c6da93aaa1

Aliases

arxiv: 1310.6882 · arxiv_version: 1310.6882v1 · doi: 10.48550/arxiv.1310.6882 · pith_short_12: T54PQWQBNDO3 · pith_short_16: T54PQWQBNDO37H4X · pith_short_8: T54PQWQB

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/T54PQWQBNDO37H4XQQQQXHPWAD \
  | 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: 9f78f85a0168ddbf9f9784210b9df600c34895198d075ae98cf0a1c6da93aaa1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87319404f3ff6b6bac3bfafb60079e73b0e5e07b029d391f967211f6cacba8f5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2013-10-25T11:33:48Z",
    "title_canon_sha256": "4bcfaa787e44e15f647b003318e9ca8c16761e395c3e25af5dcbf67a3d501425"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.6882",
    "kind": "arxiv",
    "version": 1
  }
}