Pith Number

pith:4ZAJWLND

pith:2017:4ZAJWLNDTTBDTUZ6BVOWPHZCO6

not attested not anchored not stored refs pending

Sub-wavelength focusing of acoustic waves in bubbly media

Brian Fitzpatrick, David Gontier, Habib Ammari, Hai Zhang, Hyundae Lee

arxiv:1706.08113 v1 · 2017-06-25 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4ZAJWLNDTTBDTUZ6BVOWPHZCO6}

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	2026-05-18T00:24:17.239294Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6409b2da39cc239d33e0d5d679f22778c873eb64343618dc5b3981e46234e2f

Aliases

arxiv: 1706.08113 · arxiv_version: 1706.08113v1 · doi: 10.48550/arxiv.1706.08113 · pith_short_12: 4ZAJWLNDTTBD · pith_short_16: 4ZAJWLNDTTBDTUZ6 · pith_short_8: 4ZAJWLND

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/4ZAJWLNDTTBDTUZ6BVOWPHZCO6 \
  | 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: e6409b2da39cc239d33e0d5d679f22778c873eb64343618dc5b3981e46234e2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8560f30f13d9b01b2949bef5a2ff97bd1fe97fb3f6d46d6142d94cce7219c298",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-06-25T14:14:36Z",
    "title_canon_sha256": "6d6dbc70435f720ef41d85ebcc81022b6aad9957491c9d1fc3c9f7551e63989d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.08113",
    "kind": "arxiv",
    "version": 1
  }
}