Pith Number

pith:UHYLTP4X

pith:2016:UHYLTP4X5DXRZTI3TM2D6QJ2UX

not attested not anchored not stored refs pending

Virtual pro-$p$ properties of 3-manifold groups

Gareth Wilkes

arxiv:1607.04088 v1 · 2016-07-14 · math.GR · 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{UHYLTP4X5DXRZTI3TM2D6QJ2UX}

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	2026-05-18T01:11:04.139052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a1f0b9bf97e8ef1ccd1b9b343f413aa5c22cb7ecf1e5de527e71123859542856

Aliases

arxiv: 1607.04088 · arxiv_version: 1607.04088v1 · doi: 10.48550/arxiv.1607.04088 · pith_short_12: UHYLTP4X5DXR · pith_short_16: UHYLTP4X5DXRZTI3 · pith_short_8: UHYLTP4X

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/UHYLTP4X5DXRZTI3TM2D6QJ2UX \
  | 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: a1f0b9bf97e8ef1ccd1b9b343f413aa5c22cb7ecf1e5de527e71123859542856

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e96b1850003953d8be04582ae1c8dbc9c7485d93af59b51b9c748e82cbf769d",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-07-14T11:14:41Z",
    "title_canon_sha256": "4de9144fc5952bfd1bf2ef7ccbd5979ebb011f90aa682b8d4e6f6b7c54289317"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.04088",
    "kind": "arxiv",
    "version": 1
  }
}