Pith Number

pith:AYRRXVRC

pith:2013:AYRRXVRCDGWXRM3RPBLOQWMBIR

not attested not anchored not stored refs pending

High-frequency homogenization of zero frequency stop band photonic and phononic crystals

Richard Craster, Sebastien Guenneau, Tryfon Antonakakis

arxiv:1304.5782 v1 · 2013-04-21 · physics.optics

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AYRRXVRCDGWXRM3RPBLOQWMBIR}

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	2026-05-18T01:50:23.954503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06231bd62219ad78b3717856e85981446b8937bd5d07e8b88cbcd1ec708b554c

Aliases

arxiv: 1304.5782 · arxiv_version: 1304.5782v1 · doi: 10.48550/arxiv.1304.5782 · pith_short_12: AYRRXVRCDGWX · pith_short_16: AYRRXVRCDGWXRM3R · pith_short_8: AYRRXVRC

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/AYRRXVRCDGWXRM3RPBLOQWMBIR \
  | 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: 06231bd62219ad78b3717856e85981446b8937bd5d07e8b88cbcd1ec708b554c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e945189f58327170175f10cf7560dfe19e86a5ac9bcababf26c728732b88f204",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2013-04-21T19:18:51Z",
    "title_canon_sha256": "415e3fd26aa3ab790f6c3eaad339e7d4a9c6b79c69ad1ee46f44d686f47dd9cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.5782",
    "kind": "arxiv",
    "version": 1
  }
}