Pith Number

pith:5EB33FYY

pith:2012:5EB33FYYCYTQYZEUMNTPH6QKBL

not attested not anchored not stored refs pending

A geometric proof of the Milnor conjecture

Vyacheslav Krushkal

arxiv:1205.3141 v2 · 2012-05-14 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5EB33FYYCYTQYZEUMNTPH6QKBL}

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	2026-05-18T03:55:13.621952Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e903bd971816270c64946366f3fa0a0ad7944104a36ef00a7072e139247b8a44

Aliases

arxiv: 1205.3141 · arxiv_version: 1205.3141v2 · doi: 10.48550/arxiv.1205.3141 · pith_short_12: 5EB33FYYCYTQ · pith_short_16: 5EB33FYYCYTQYZEU · pith_short_8: 5EB33FYY

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/5EB33FYYCYTQYZEUMNTPH6QKBL \
  | 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: e903bd971816270c64946366f3fa0a0ad7944104a36ef00a7072e139247b8a44

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "be1a36d1f8406eb5d97b8618da947cc2a176aa8ef4e3b27235c56a525bcb609b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-05-14T19:14:00Z",
    "title_canon_sha256": "8a1322c7d407f49c45fabf697fdb33d03b19135092f21f17aafe76bc7e112a99"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.3141",
    "kind": "arxiv",
    "version": 2
  }
}