Pith Number

pith:EYEYZE6P

pith:2022:EYEYZE6PRSYSRPODQU3OJDTR2R

not attested not anchored not stored refs pending

Optimal estimate of field concentration between multiscale nearly-touching inclusions for 3-D Helmholtz system

Hongyu Liu, Wanjing Tang, Youjun Deng, Yueguang Hu

arxiv:2211.05609 v2 · 2022-11-10 · 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{EYEYZE6PRSYSRPODQU3OJDTR2R}

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	2026-07-05T05:16:38.356636Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26098c93cf8cb128bdc38536e48e71d44feac695aab7019701d7dd0e9af95205

Aliases

arxiv: 2211.05609 · arxiv_version: 2211.05609v2 · doi: 10.48550/arxiv.2211.05609 · pith_short_12: EYEYZE6PRSYS · pith_short_16: EYEYZE6PRSYSRPOD · pith_short_8: EYEYZE6P

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/EYEYZE6PRSYSRPODQU3OJDTR2R \
  | 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: 26098c93cf8cb128bdc38536e48e71d44feac695aab7019701d7dd0e9af95205

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dc696d9572e8ea458d4cf5b782af39687acd8076f7e4bbdd50faa707206ea5ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-11-10T14:30:31Z",
    "title_canon_sha256": "eb0ce89ffae45a00547a7bdf8c2a4641a36cd2976b14915c3241a348b33ade86"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2211.05609",
    "kind": "arxiv",
    "version": 2
  }
}