Pith Number

pith:WBBVV4WL

pith:2017:WBBVV4WLUSMTWZJI4R7MQJMJQA

not attested not anchored not stored refs pending

Bloch waves in bubbly crystal near the first band gap: a high-frequency homogenization approach

Habib Ammari, Hai Zhang, Hyundae Lee

arxiv:1708.07955 v2 · 2017-08-26 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WBBVV4WLUSMTWZJI4R7MQJMJQA}

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	2026-05-18T00:25:07.530221Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b0435af2cba4993b6528e47ec82589803fb1fa18c12c7278d2b0e2dd3c44e868

Aliases

arxiv: 1708.07955 · arxiv_version: 1708.07955v2 · doi: 10.48550/arxiv.1708.07955 · pith_short_12: WBBVV4WLUSMT · pith_short_16: WBBVV4WLUSMTWZJI · pith_short_8: WBBVV4WL

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/WBBVV4WLUSMTWZJI4R7MQJMJQA \
  | 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: b0435af2cba4993b6528e47ec82589803fb1fa18c12c7278d2b0e2dd3c44e868

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ebb4321d95ed03a223e4088d8aeaea412abfad35d1489b0ea4b83bff2c96b787",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-08-26T09:15:58Z",
    "title_canon_sha256": "713fea12353b1c30eb3d5787e998b6aa2f495d24c7bf59ae207e8cf72358463e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.07955",
    "kind": "arxiv",
    "version": 2
  }
}