Pith Number

pith:M63IIIFZ

pith:2026:M63IIIFZ66IV7ZAQX7HJZJCSOS

not attested not anchored not stored refs pending

Minnaert resonances and higher-order acoustic modes for bubbles in a viscous fluid with surface tension

Habib Ammari, Hongjie Li, Wenjia Jing, Xin Fu

arxiv:2606.21070 v1 · 2026-06-19 · 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{M63IIIFZ66IV7ZAQX7HJZJCSOS}

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	2026-06-23T01:12:28.872995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67b68420b9f7915fe410bfce9ca4527486d39422380922854ccfc3773a5df79f

Aliases

arxiv: 2606.21070 · arxiv_version: 2606.21070v1 · doi: 10.48550/arxiv.2606.21070 · pith_short_12: M63IIIFZ66IV · pith_short_16: M63IIIFZ66IV7ZAQ · pith_short_8: M63IIIFZ

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/M63IIIFZ66IV7ZAQX7HJZJCSOS \
  | 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: 67b68420b9f7915fe410bfce9ca4527486d39422380922854ccfc3773a5df79f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df0159a3c36aded099e4526dcf4f62608d5d612bc05629e99294a96cd2e0050a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-19T03:39:12Z",
    "title_canon_sha256": "8a290b36c515a11024e07b8cc9318d890dafe808851ba9a78b27a239f6001fe2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.21070",
    "kind": "arxiv",
    "version": 1
  }
}