Pith Number

pith:CLUWTRVC

pith:2005:CLUWTRVCG7SICGPOAZOUWWUX3M

not attested not anchored not stored refs pending

Torsion in Tiling Homology and Cohomology

Franz G\"ahler, Johannes Kellendonk, John Hunton

arxiv:math-ph/0505048 v2 · 2005-05-19 · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CLUWTRVCG7SICGPOAZOUWWUX3M}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T04:02:13.877077Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12e969c6a237e48119ee065d4b5a97db1ea1f74925462ec06433f5a1badab704

Aliases

arxiv: math-ph/0505048 · arxiv_version: math-ph/0505048v2 · doi: 10.48550/arxiv.math-ph/0505048 · pith_short_12: CLUWTRVCG7SI · pith_short_16: CLUWTRVCG7SICGPO · pith_short_8: CLUWTRVC

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/CLUWTRVCG7SICGPOAZOUWWUX3M \
  | 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: 12e969c6a237e48119ee065d4b5a97db1ea1f74925462ec06433f5a1badab704

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4baa6b6259db043f6cf1a8032d7b427737644ddf581d6f71e8573d1b8314071",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2005-05-19T13:08:00Z",
    "title_canon_sha256": "b2a006f15860f83b3c239163352fca9426c05349ed44f6e4dfa15e4a89a4634e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0505048",
    "kind": "arxiv",
    "version": 2
  }
}