Pith Number

pith:PEP2B2NV

pith:2015:PEP2B2NV56FNGAOE6UD4FILZ3L

not attested not anchored not stored refs pending

Beyond Endoscopy via the trace formula - III: The standard representation

Salim Ali Altug

arxiv:1512.09249 v1 · 2015-12-31 · math.NT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PEP2B2NV56FNGAOE6UD4FILZ3L}

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	2026-05-18T01:23:32.882829Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

791fa0e9b5ef8ad301c4f507c2a179daca6b04eec04d45b0e2db1da4ce81dc18

Aliases

arxiv: 1512.09249 · arxiv_version: 1512.09249v1 · doi: 10.48550/arxiv.1512.09249 · pith_short_12: PEP2B2NV56FN · pith_short_16: PEP2B2NV56FNGAOE · pith_short_8: PEP2B2NV

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/PEP2B2NV56FNGAOE6UD4FILZ3L \
  | 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: 791fa0e9b5ef8ad301c4f507c2a179daca6b04eec04d45b0e2db1da4ce81dc18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7dcb430c2c713213faaf5540d1318f23bb7096343f383b4825282870eb4bafd",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-12-31T10:15:06Z",
    "title_canon_sha256": "5eed1843478d3ac8f1c26bff8a3b698fdc53dcf92a76f21d2fcec8508f6fe8f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.09249",
    "kind": "arxiv",
    "version": 1
  }
}