Pith Number

pith:ALVHO6PD

pith:2018:ALVHO6PDNMN64ZP6YP75EAK3CX

not attested not anchored not stored refs pending

Revisiting Leighton's Theorem with the Haar Measure

Daniel J. Woodhouse

arxiv:1806.08196 v2 · 2018-06-21 · 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{ALVHO6PDNMN64ZP6YP75EAK3CX}

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	2026-05-18T00:09:35.455277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02ea7779e36b1bee65fec3ffd2015b15ea3c00672e704226cd590a7f7c39d53a

Aliases

arxiv: 1806.08196 · arxiv_version: 1806.08196v2 · doi: 10.48550/arxiv.1806.08196 · pith_short_12: ALVHO6PDNMN6 · pith_short_16: ALVHO6PDNMN64ZP6 · pith_short_8: ALVHO6PD

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/ALVHO6PDNMN64ZP6YP75EAK3CX \
  | 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: 02ea7779e36b1bee65fec3ffd2015b15ea3c00672e704226cd590a7f7c39d53a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dc4a2f405b35218a5f96e46727ffaf55cd1347fb48ae347e185b2ee9efa84ab",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-06-21T12:25:19Z",
    "title_canon_sha256": "af083d76ced7a2338353f2e3a8a1ac7ff8f8395057643787cda89bf3869f6fa0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.08196",
    "kind": "arxiv",
    "version": 2
  }
}