Pith Number

pith:ZJUCX3LF

pith:2009:ZJUCX3LFU3AWLA4F3HO3IMYMJJ

not attested not anchored not stored refs pending

Derivatives of the identity and generalizations of Milnor's invariants

Brian A. Munson

arxiv:0909.3074 v2 · 2009-09-16 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZJUCX3LFU3AWLA4F3HO3IMYMJJ}

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	2026-05-18T02:58:02.776695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ca682bed65a6c1658385d9ddb4330c4a6631589c6cd32e6b6e2f12390c60215a

Aliases

arxiv: 0909.3074 · arxiv_version: 0909.3074v2 · doi: 10.48550/arxiv.0909.3074 · pith_short_12: ZJUCX3LFU3AW · pith_short_16: ZJUCX3LFU3AWLA4F · pith_short_8: ZJUCX3LF

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/ZJUCX3LFU3AWLA4F3HO3IMYMJJ \
  | 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: ca682bed65a6c1658385d9ddb4330c4a6631589c6cd32e6b6e2f12390c60215a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e56fb0bb1dbe17ec960c56fc7cd9ae9ecc3c315b1815b5c01308bbd0767031fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2009-09-16T17:56:52Z",
    "title_canon_sha256": "bfecb14cd72b5f23aed3b5b0075849393aa1052e256843f05f266f10f62bcf9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.3074",
    "kind": "arxiv",
    "version": 2
  }
}