Pith Number

pith:3LFQZ4ZO

pith:2013:3LFQZ4ZOSYVIOBZLAGRG6YUH6T

not attested not anchored not stored refs pending

$PD_4$-complexes and 2-dimensional duality groups

Jonathan A. Hillman

arxiv:1303.5486 v8 · 2013-03-21 · 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{3LFQZ4ZOSYVIOBZLAGRG6YUH6T}

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	2026-05-18T02:45:20.886780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dacb0cf32e962a87072b01a26f6287f4d927422124bf7653f95cb31059546cec

Aliases

arxiv: 1303.5486 · arxiv_version: 1303.5486v8 · doi: 10.48550/arxiv.1303.5486 · pith_short_12: 3LFQZ4ZOSYVI · pith_short_16: 3LFQZ4ZOSYVIOBZL · pith_short_8: 3LFQZ4ZO

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/3LFQZ4ZOSYVIOBZLAGRG6YUH6T \
  | 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: dacb0cf32e962a87072b01a26f6287f4d927422124bf7653f95cb31059546cec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6025b3ec19c7ebf1695ed7bb7e7009d2e8c71cac200de5bf27ca641f0a36ec8f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-03-21T23:53:07Z",
    "title_canon_sha256": "bf961b2bcd560300922b1eaf526d9cf902cad924667528a1799842017b070d73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.5486",
    "kind": "arxiv",
    "version": 8
  }
}