Pith Number

pith:G5GRVILQ

pith:2012:G5GRVILQQOFB2F7ERBQOGJYR5N

not attested not anchored not stored refs pending

Approximation of the integrated density of states on sofic groups

Christoph Schumacher, Fabian Schwarzenberger

arxiv:1212.5207 v1 · 2012-12-20 · math.SP · 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{G5GRVILQQOFB2F7ERBQOGJYR5N}

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	2026-05-18T03:38:03.171858Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

374d1aa170838a1d17e48860e32711eb50938a288d9e665da403bed997b17a4e

Aliases

arxiv: 1212.5207 · arxiv_version: 1212.5207v1 · doi: 10.48550/arxiv.1212.5207 · pith_short_12: G5GRVILQQOFB · pith_short_16: G5GRVILQQOFB2F7E · pith_short_8: G5GRVILQ

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/G5GRVILQQOFB2F7ERBQOGJYR5N \
  | 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: 374d1aa170838a1d17e48860e32711eb50938a288d9e665da403bed997b17a4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "118b2051db3893f97c833aae0d7346b89728c08d076c42adc30134d8b1ec3cf1",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-12-20T19:50:22Z",
    "title_canon_sha256": "fff367f2dc6ada9b14738134e5f5bb65a382079faa22620ffaa4bafd5a4f3564"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.5207",
    "kind": "arxiv",
    "version": 1
  }
}