Pith Number

pith:DLDDR7FV

pith:2011:DLDDR7FVTPEYUF33S6EJDTRLXU

not attested not anchored not stored refs pending

The Milnor $\bar{\mu}$ invariants and nanophrases

Yuka Kotorii

arxiv:1110.3887 v4 · 2011-10-18 · 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{DLDDR7FVTPEYUF33S6EJDTRLXU}

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	2026-05-18T03:28:17.702258Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ac638fcb59bc98a177b978891ce2bbd35ed0c90dbdcb84218878a9be00df1b8

Aliases

arxiv: 1110.3887 · arxiv_version: 1110.3887v4 · doi: 10.48550/arxiv.1110.3887 · pith_short_12: DLDDR7FVTPEY · pith_short_16: DLDDR7FVTPEYUF33 · pith_short_8: DLDDR7FV

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/DLDDR7FVTPEYUF33S6EJDTRLXU \
  | 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: 1ac638fcb59bc98a177b978891ce2bbd35ed0c90dbdcb84218878a9be00df1b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1021b83f874a253e5d17a05ed529f78167583ad755e05e3da940bdeae21a834f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-10-18T07:00:33Z",
    "title_canon_sha256": "5ca977ff2c0b5303df7c75094da359f4ff89aa12dd6dacf7919a8b1f2fef84f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.3887",
    "kind": "arxiv",
    "version": 4
  }
}