Pith Number

pith:F6EFWPKC

pith:2013:F6EFWPKCCU4DKZOMQT3BRLH6LX

not attested not anchored not stored refs pending

Uniform estimates of nonlinear spectral gaps

Takefumi Kondo, Tetsu Toyoda

arxiv:1308.4493 v2 · 2013-08-21 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F6EFWPKCCU4DKZOMQT3BRLH6LX}

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	2026-05-18T01:49:56.174238Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f885b3d4215383565cc84f618acfe5dfdb44fe75113ec0d86929e7aeed1c893

Aliases

arxiv: 1308.4493 · arxiv_version: 1308.4493v2 · doi: 10.48550/arxiv.1308.4493 · pith_short_12: F6EFWPKCCU4D · pith_short_16: F6EFWPKCCU4DKZOM · pith_short_8: F6EFWPKC

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/F6EFWPKCCU4DKZOMQT3BRLH6LX \
  | 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: 2f885b3d4215383565cc84f618acfe5dfdb44fe75113ec0d86929e7aeed1c893

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "433a3bbd86264a9a1b768f677ab83c6bf133205b177070627a514f8f58d364ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-08-21T06:29:44Z",
    "title_canon_sha256": "8f70ebdb06822f15d041ef8c8fe21c14591f89c1595129fe79a10db04c316f12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.4493",
    "kind": "arxiv",
    "version": 2
  }
}