Pith Number

pith:A24KLO2I

pith:2017:A24KLO2IXUQ7PEB4NPE5IDIAHS

not attested not anchored not stored refs pending

Completeness of the set $\{e^{ik\beta \cdot s}\}|_{\forall \beta \in S^2}$

A. G. Ramm

arxiv:1706.00403 v1 · 2017-05-21 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A24KLO2IXUQ7PEB4NPE5IDIAHS}

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	2026-05-18T00:43:14.135030Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06b8a5bb48bd21f7903c6bc9d40d003cbd09f3c59aab418c135a5f9920606415

Aliases

arxiv: 1706.00403 · arxiv_version: 1706.00403v1 · doi: 10.48550/arxiv.1706.00403 · pith_short_12: A24KLO2IXUQ7 · pith_short_16: A24KLO2IXUQ7PEB4 · pith_short_8: A24KLO2I

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/A24KLO2IXUQ7PEB4NPE5IDIAHS \
  | 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: 06b8a5bb48bd21f7903c6bc9d40d003cbd09f3c59aab418c135a5f9920606415

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9136c68c6f6275df6ecfb0a64976afba81323184caf2311db296937dfa4f014b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-05-21T17:34:58Z",
    "title_canon_sha256": "63d9ccfadd56c3931ed813562af8de27ebd77cd6b9ca2d365ca3e306faed020b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.00403",
    "kind": "arxiv",
    "version": 1
  }
}