Pith Number

pith:TAZB76EX

pith:2014:TAZB76EXXGYTC7DT4JZMKKBUA7

not attested not anchored not stored refs pending

The total Milnor number of the weighted-Le-Yomdin-at-infinity polynomial

Yongqiang Liu

arxiv:1412.7688 v2 · 2014-12-24 · math.AT · 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{TAZB76EXXGYTC7DT4JZMKKBUA7}

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	2026-05-18T02:30:07.546984Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98321ff897b9b1317c73e272c5283407dc1ca9f496858551ac8f45c0c1bd455a

Aliases

arxiv: 1412.7688 · arxiv_version: 1412.7688v2 · doi: 10.48550/arxiv.1412.7688 · pith_short_12: TAZB76EXXGYT · pith_short_16: TAZB76EXXGYTC7DT · pith_short_8: TAZB76EX

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/TAZB76EXXGYTC7DT4JZMKKBUA7 \
  | 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: 98321ff897b9b1317c73e272c5283407dc1ca9f496858551ac8f45c0c1bd455a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b14cd0513f933471faa71ed62b09ea549cc9ea8ef9356febc8a319b885f08de",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2014-12-24T15:28:00Z",
    "title_canon_sha256": "ea36810c583f5767f3559239a5a0d68234e1ab8b7adcf29eddbe0dd2e9e77978"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.7688",
    "kind": "arxiv",
    "version": 2
  }
}