Pith Number

pith:GIRAVMQD

pith:2006:GIRAVMQD7QOHIQJLTNSVXBTJXF

not attested not anchored not stored refs pending

On Spin Structures and Dirac Operators on the Noncommutative Torus

Andrzej Sitarz, Mario Paschke

arxiv:math/0605191 v1 · 2006-05-08 · math.QA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GIRAVMQD7QOHIQJLTNSVXBTJXF}

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	2026-05-18T00:14:23.471398Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32220ab203fc1c74412b9b655b8669b96cf63ba63424a9ef4e9f839362137c0b

Aliases

arxiv: math/0605191 · arxiv_version: math/0605191v1 · doi: 10.48550/arxiv.math/0605191 · pith_short_12: GIRAVMQD7QOH · pith_short_16: GIRAVMQD7QOHIQJL · pith_short_8: GIRAVMQD

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/GIRAVMQD7QOHIQJLTNSVXBTJXF \
  | 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: 32220ab203fc1c74412b9b655b8669b96cf63ba63424a9ef4e9f839362137c0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa51514c335750172290ad529651a5c9a83ef3882bbe4b706c7c1ed310a9f7fc",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.QA",
    "submitted_at": "2006-05-08T09:12:43Z",
    "title_canon_sha256": "beb53918daf2ee6575a15603eece778b3d61aa7d1a9c92db2b2d3896aa9d5f98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0605191",
    "kind": "arxiv",
    "version": 1
  }
}