Pith Number

pith:ZT4EDAPA

pith:2018:ZT4EDAPA42V6PZBN4K47ITYHVL

not attested not anchored not stored refs pending

On the Milnor formula in arbitrary characteristic

Arkadiusz P{\l}oski, Evelia R. Garc\'ia Barroso

arxiv:1812.06512 v1 · 2018-12-16 · 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{ZT4EDAPA42V6PZBN4K47ITYHVL}

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	2026-05-17T23:58:10.031264Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccf84181e0e6abe7e42de2b9f44f07aafd9f520046972d352ea8f0469aeaab94

Aliases

arxiv: 1812.06512 · arxiv_version: 1812.06512v1 · doi: 10.48550/arxiv.1812.06512 · pith_short_12: ZT4EDAPA42V6 · pith_short_16: ZT4EDAPA42V6PZBN · pith_short_8: ZT4EDAPA

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/ZT4EDAPA42V6PZBN4K47ITYHVL \
  | 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: ccf84181e0e6abe7e42de2b9f44f07aafd9f520046972d352ea8f0469aeaab94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b77c661edd420e567976f50232b6a9bb59075cbb88236007f42d6e8601b53b20",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2018-12-16T18:07:11Z",
    "title_canon_sha256": "371bbf847fee7c443310d019dd43fe5cbe99fbcfe1831f1eccb46c5cbc5065ed"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.06512",
    "kind": "arxiv",
    "version": 1
  }
}