Pith Number

pith:HKR6LL5B

pith:2017:HKR6LL5B7YBQNW4Y2PSTV2RMRB

not attested not anchored not stored refs pending

Discrete fundamental groups of Warped Cones and expanders

Federico Vigolo

arxiv:1710.04955 v3 · 2017-10-13 · math.MG · 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{HKR6LL5B7YBQNW4Y2PSTV2RMRB}

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	2026-05-18T00:02:19.508929Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3aa3e5afa1fe0306db98d3e53aea2c885f3745d70e5fc7a00765661a87708e95

Aliases

arxiv: 1710.04955 · arxiv_version: 1710.04955v3 · doi: 10.48550/arxiv.1710.04955 · pith_short_12: HKR6LL5B7YBQ · pith_short_16: HKR6LL5B7YBQNW4Y · pith_short_8: HKR6LL5B

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/HKR6LL5B7YBQNW4Y2PSTV2RMRB \
  | 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: 3aa3e5afa1fe0306db98d3e53aea2c885f3745d70e5fc7a00765661a87708e95

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9573911ffa4c781d18c87578426227be6fd82815ba71c4dfa8ef5e74d20c5173",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2017-10-13T15:07:15Z",
    "title_canon_sha256": "4c626da831231edd3ec22c6c5f19598a3a5d41bd9ae0a571d443cee0590817c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.04955",
    "kind": "arxiv",
    "version": 3
  }
}