Pith Number

pith:ESYIJ5HV

pith:2026:ESYIJ5HVALLC6DTOZHSLQTVLB3

not attested not anchored not stored refs pending

Limiting Absorption Principle for the Helmholtz Equation with Sign-Changing Coefficients in Multilayer Spheres

Wenjing Zhang, Yixian Gao

arxiv:2605.24826 v1 · 2026-05-24 · 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{ESYIJ5HVALLC6DTOZHSLQTVLB3}

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	2026-05-26T01:04:00.395617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24b084f4f502d62f0e6ec9e4b84eab0ed7f0eeeb30b00bd120ed9851a73fdbda

Aliases

arxiv: 2605.24826 · arxiv_version: 2605.24826v1 · doi: 10.48550/arxiv.2605.24826 · pith_short_12: ESYIJ5HVALLC · pith_short_16: ESYIJ5HVALLC6DTO · pith_short_8: ESYIJ5HV

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/ESYIJ5HVALLC6DTOZHSLQTVLB3 \
  | 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: 24b084f4f502d62f0e6ec9e4b84eab0ed7f0eeeb30b00bd120ed9851a73fdbda

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "669fef5499d8c54c0f0252792a3d84f7d39b84009cc08bc32fe4d0f3341eec72",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-24T02:39:29Z",
    "title_canon_sha256": "4bf7d269d435597393b978b1b94ebf057ed84451c8a5b5e84e307f2dc073d34a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.24826",
    "kind": "arxiv",
    "version": 1
  }
}