Pith Number

pith:QQ5MJ3U3

pith:2010:QQ5MJ3U3JUWCLA2ACI5L7AZVFV

not attested not anchored not stored refs pending

Levinson's theorem and higher degree traces for Aharonov-Bohm operators

J. Kellendonk, K. Pankrashkin, S. Richard

arxiv:1012.3215 v1 · 2010-12-15 · 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{QQ5MJ3U3JUWCLA2ACI5L7AZVFV}

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	2026-05-18T02:04:24.657515Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

843ac4ee9b4d2c258340123abf83352d57223da443265cd7a98bf55611db9bd1

Aliases

arxiv: 1012.3215 · arxiv_version: 1012.3215v1 · doi: 10.48550/arxiv.1012.3215 · pith_short_12: QQ5MJ3U3JUWC · pith_short_16: QQ5MJ3U3JUWCLA2A · pith_short_8: QQ5MJ3U3

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/QQ5MJ3U3JUWCLA2ACI5L7AZVFV \
  | 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: 843ac4ee9b4d2c258340123abf83352d57223da443265cd7a98bf55611db9bd1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f576509b7f182c16fa04d8f19905a6f47454514236fd5f00a54cd8a5bb11cef4",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-12-15T02:49:31Z",
    "title_canon_sha256": "dc5f7832e9c964770975b64a95d11cbdc0f36ef7e82c58e05a9ba75b398d500c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3215",
    "kind": "arxiv",
    "version": 1
  }
}