Pith Number

pith:Q7RTY5FR

pith:2011:Q7RTY5FRCTMZVR5UW52V4CGZHA

not attested not anchored not stored refs pending

Minimal capacity points and the Lowest eigenfunctions

Jia Pan, Mark Levi

arxiv:1104.0555 v1 · 2011-04-04 · math.CA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q7RTY5FRCTMZVR5UW52V4CGZHA}

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	2026-05-18T02:22:11.205130Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87e33c74b114d99ac7b4b7755e08d9381d56d48b936fb70b9ea0cb9310a1e769

Aliases

arxiv: 1104.0555 · arxiv_version: 1104.0555v1 · doi: 10.48550/arxiv.1104.0555 · pith_short_12: Q7RTY5FRCTMZ · pith_short_16: Q7RTY5FRCTMZVR5U · pith_short_8: Q7RTY5FR

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/Q7RTY5FRCTMZVR5UW52V4CGZHA \
  | 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: 87e33c74b114d99ac7b4b7755e08d9381d56d48b936fb70b9ea0cb9310a1e769

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32617f9c5c0d4904db4bd597923bbb335fcccca8370b255cee4e2fef28228bdc",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-04-04T13:02:37Z",
    "title_canon_sha256": "6538eb420f74ac7836cf9a0362a98f5e4f2648483247f69045321fc5e8e6e65f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.0555",
    "kind": "arxiv",
    "version": 1
  }
}