Pith Number

pith:FVKBTALB

pith:2013:FVKBTALB6G4EV2TRG763KTIZOC

not attested not anchored not stored refs pending

Cubulating hyperbolic free-by-cyclic groups: the irreducible case

Daniel T. Wise, Mark F. Hagen

arxiv:1311.2084 v3 · 2013-11-08 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FVKBTALB6G4EV2TRG763KTIZOC}

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	2026-05-18T01:08:44.958838Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d54198161f1b84aea7137fdb54d19708e6f614e26b5defccb2980fec0cc7c18

Aliases

arxiv: 1311.2084 · arxiv_version: 1311.2084v3 · doi: 10.48550/arxiv.1311.2084 · pith_short_12: FVKBTALB6G4E · pith_short_16: FVKBTALB6G4EV2TR · pith_short_8: FVKBTALB

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/FVKBTALB6G4EV2TRG763KTIZOC \
  | 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: 2d54198161f1b84aea7137fdb54d19708e6f614e26b5defccb2980fec0cc7c18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b1f56247d1016c8563ba02933979d71e8bff52a202710fbc08c0ce7c8edad72",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-11-08T21:15:34Z",
    "title_canon_sha256": "bebbc4e9a4a3b1b66e67d77af5342769d4a6e33a9dea73723d23e03ec209a27d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.2084",
    "kind": "arxiv",
    "version": 3
  }
}