Pith Number

pith:GCRNOKHQ

pith:2013:GCRNOKHQAO2MYSGXAIP64RLSVC

not attested not anchored not stored refs pending

Lattices in products of trees and a theorem of H.C. Wang

Marc Burger, Shahar Mozes

arxiv:1305.4922 v2 · 2013-05-21 · 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{GCRNOKHQAO2MYSGXAIP64RLSVC}

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	2026-05-18T00:45:08.875304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30a2d728f003b4cc48d7021fee4572a8a5d39634c4325a04c9e3db33e40b01eb

Aliases

arxiv: 1305.4922 · arxiv_version: 1305.4922v2 · doi: 10.48550/arxiv.1305.4922 · pith_short_12: GCRNOKHQAO2M · pith_short_16: GCRNOKHQAO2MYSGX · pith_short_8: GCRNOKHQ

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/GCRNOKHQAO2MYSGXAIP64RLSVC \
  | 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: 30a2d728f003b4cc48d7021fee4572a8a5d39634c4325a04c9e3db33e40b01eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6597f1c19552526b1d5917337a886cb56375e2be6dc69ca71833db5c704b480",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-05-21T19:19:49Z",
    "title_canon_sha256": "9792cd983cd009bc2e44d3597edb5857e19412bdecc596e75b051ac8b91abf29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.4922",
    "kind": "arxiv",
    "version": 2
  }
}