Pith Number

pith:S26K64H6

pith:2017:S26K64H6UQ6LGDM2GTUA2KXNAF

not attested not anchored not stored refs pending

Counting problems in graph products and relatively hyperbolic groups

Giulio Tiozzo, Ilya Gekhtman, Samuel J. Taylor

arxiv:1711.04177 v1 · 2017-11-11 · math.GT · math.DS · 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{S26K64H6UQ6LGDM2GTUA2KXNAF}

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	2026-05-18T00:30:39.861889Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96bcaf70fea43cb30d9a34e80d2aed014247e3f14a82fabf6fe7489c25211d52

Aliases

arxiv: 1711.04177 · arxiv_version: 1711.04177v1 · doi: 10.48550/arxiv.1711.04177 · pith_short_12: S26K64H6UQ6L · pith_short_16: S26K64H6UQ6LGDM2 · pith_short_8: S26K64H6

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/S26K64H6UQ6LGDM2GTUA2KXNAF \
  | 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: 96bcaf70fea43cb30d9a34e80d2aed014247e3f14a82fabf6fe7489c25211d52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0193d7ebca6fda3c8c3b03b1b961602191a9a20e1695b285bfad4206937eb479",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2017-11-11T18:03:02Z",
    "title_canon_sha256": "e96909e432a94b2d90dc73e8e565e0f192d929eeff9e4091e1f4b5749e8a45db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1711.04177",
    "kind": "arxiv",
    "version": 1
  }
}