Pith Number

pith:BLLX7MY4

pith:2010:BLLX7MY4NIAOB3K45ELGTV7LHF

not attested not anchored not stored refs pending

On the spectrum of a waveguide with periodic cracks

Konstantin Pankrashkin

arxiv:1007.3656 v1 · 2010-07-21 · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BLLX7MY4NIAOB3K45ELGTV7LHF}

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	2026-05-18T02:06:12.013605Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ad77fb31c6a00e0ed5ce91669d7eb39653b7635a34849cc2253d33f4ef64590

Aliases

arxiv: 1007.3656 · arxiv_version: 1007.3656v1 · doi: 10.48550/arxiv.1007.3656 · pith_short_12: BLLX7MY4NIAO · pith_short_16: BLLX7MY4NIAOB3K4 · pith_short_8: BLLX7MY4

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/BLLX7MY4NIAOB3K45ELGTV7LHF \
  | 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: 0ad77fb31c6a00e0ed5ce91669d7eb39653b7635a34849cc2253d33f4ef64590

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e47941eff94b415fe80fa00b72c569e57116b2fefde777fe44b33710ab88b09",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2010-07-21T13:41:01Z",
    "title_canon_sha256": "d2cb1aa86fec8e73d8d7afdb4a7aa9d6231cfbcba0f36cdf2df5ef555ffb661d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.3656",
    "kind": "arxiv",
    "version": 1
  }
}