Pith Number

pith:NI4PFRD6

pith:2010:NI4PFRD6X7H2R7VMTSVMMW7N5N

not attested not anchored not stored refs pending

On spectral action over Bieberbach manifolds

Andrzej Sitarz, Piotr Olczykowski

arxiv:1012.0136 v1 · 2010-12-01 · math-ph · hep-th · math.MP · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NI4PFRD6X7H2R7VMTSVMMW7N5N}

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	2026-05-18T04:13:56.737549Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a38f2c47ebfcfa8feac9caac65bedeb771aa6cf1d36183c61382285f37b8614

Aliases

arxiv: 1012.0136 · arxiv_version: 1012.0136v1 · doi: 10.48550/arxiv.1012.0136 · pith_short_12: NI4PFRD6X7H2 · pith_short_16: NI4PFRD6X7H2R7VM · pith_short_8: NI4PFRD6

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/NI4PFRD6X7H2R7VMTSVMMW7N5N \
  | 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: 6a38f2c47ebfcfa8feac9caac65bedeb771aa6cf1d36183c61382285f37b8614

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc2bbec1ca8290c3ccebc2574aee6eaf33106cd96c9228f78ea30240baf80bae",
    "cross_cats_sorted": [
      "hep-th",
      "math.MP",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-12-01T09:40:40Z",
    "title_canon_sha256": "210564279073a81baf23ef54bd28673fd5500946664fe81dcf63da3ad40821b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0136",
    "kind": "arxiv",
    "version": 1
  }
}