Pith Number

pith:5TUKCQ7Z

pith:2014:5TUKCQ7ZQSGSDCULTUSDSZRDJH

not attested not anchored not stored refs pending

Unexpected Spectral Asymptotics for Wave Equations on certain Compact Spacetimes

Jonathan Fox, Robert S. Strichartz

arxiv:1407.2517 v1 · 2014-07-09 · 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{5TUKCQ7ZQSGSDCULTUSDSZRDJH}

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	2026-05-18T02:48:01.409753Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ece8a143f9848d218a8b9d2439662349d58589290f4b458e2009432999f94bef

Aliases

arxiv: 1407.2517 · arxiv_version: 1407.2517v1 · doi: 10.48550/arxiv.1407.2517 · pith_short_12: 5TUKCQ7ZQSGS · pith_short_16: 5TUKCQ7ZQSGSDCUL · pith_short_8: 5TUKCQ7Z

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/5TUKCQ7ZQSGSDCULTUSDSZRDJH \
  | 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: ece8a143f9848d218a8b9d2439662349d58589290f4b458e2009432999f94bef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5671e59ccfd05f651936e270b9549216df62df6e79581619145a84a23e56c193",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-07-09T15:11:42Z",
    "title_canon_sha256": "6cf60e5defd0eae746ed9868b6944711d47822747c185ccd2c408768211a89f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.2517",
    "kind": "arxiv",
    "version": 1
  }
}