Pith Number

pith:VQU2Y73O

pith:2016:VQU2Y73O2TJEGIVVORXG2BVYDQ

not attested not anchored not stored refs pending

The co-surface graph and the geometry of hyperbolic free group extensions

Samuel J. Taylor, Spencer Dowdall

arxiv:1601.00101 v2 · 2016-01-01 · math.GT · 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{VQU2Y73O2TJEGIVVORXG2BVYDQ}

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	2026-05-18T00:45:08.479142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac29ac7f6ed4d24322b5746e6d06b81c0725634cc4ecb1669337e816fafb5d3e

Aliases

arxiv: 1601.00101 · arxiv_version: 1601.00101v2 · doi: 10.48550/arxiv.1601.00101 · pith_short_12: VQU2Y73O2TJE · pith_short_16: VQU2Y73O2TJEGIVV · pith_short_8: VQU2Y73O

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/VQU2Y73O2TJEGIVVORXG2BVYDQ \
  | 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: ac29ac7f6ed4d24322b5746e6d06b81c0725634cc4ecb1669337e816fafb5d3e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c2c0afe2bcb04bccfdac27a2be55c236642e482b1bcfcb711f31301333a381c",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-01-01T18:15:58Z",
    "title_canon_sha256": "a812af9671891147ac729a74390361f123fdef464f8883b66fbcd5387eb282bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.00101",
    "kind": "arxiv",
    "version": 2
  }
}