Pith Number

pith:BIBPRKXU

pith:2026:BIBPRKXUCBIRFMVVEUCC7HDHKF

not attested not anchored not stored refs pending

Approximate eigenfunctions for some aperiodic crystals

Long Meng

arxiv:2607.08320 v1 · 2026-07-09 · math-ph · cond-mat.mes-hall · math.FA · math.MP · math.SP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BIBPRKXUCBIRFMVVEUCC7HDHKF}

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	2026-07-10T01:19:47.181812Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a02f8aaf4105112b2b525042f9c6751698fbab2d5d7bf0e843711cdf457f6fc

Aliases

arxiv: 2607.08320 · arxiv_version: 2607.08320v1 · doi: 10.48550/arxiv.2607.08320 · pith_short_12: BIBPRKXUCBIR · pith_short_16: BIBPRKXUCBIRFMVV · pith_short_8: BIBPRKXU

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/BIBPRKXUCBIRFMVVEUCC7HDHKF \
  | 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: 0a02f8aaf4105112b2b525042f9c6751698fbab2d5d7bf0e843711cdf457f6fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "32d9bfde26b0adfe691f4f3e8ca302963c7316a949bc972cb122621b757170b0",
    "cross_cats_sorted": [
      "cond-mat.mes-hall",
      "math.FA",
      "math.MP",
      "math.SP",
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-09T10:03:51Z",
    "title_canon_sha256": "fbd153cfe9a8c8ce453a6a0329410b91577c156db0674e90d746ac34ac0fef8c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.08320",
    "kind": "arxiv",
    "version": 1
  }
}