Pith Number

pith:VF6HPV2Q

pith:2025:VF6HPV2Q6SG7PAWHNUBNLIFEPP

not attested not anchored not stored refs pending

Generalized Rellich's lemmas, uniqueness theorem and inside-out duality for scattering poles

Jiguang Sun, Lei Zhang, XiaoDong Liu

arxiv:2507.04242 v1 · 2025-07-06 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VF6HPV2Q6SG7PAWHNUBNLIFEPP}

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	2026-07-05T11:32:44.113213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a97c77d750f48df782c76d02d5a0a47bda8dca17140474e4630d4d78fdf49da7

Aliases

arxiv: 2507.04242 · arxiv_version: 2507.04242v1 · doi: 10.48550/arxiv.2507.04242 · pith_short_12: VF6HPV2Q6SG7 · pith_short_16: VF6HPV2Q6SG7PAWH · pith_short_8: VF6HPV2Q

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/VF6HPV2Q6SG7PAWHNUBNLIFEPP \
  | 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: a97c77d750f48df782c76d02d5a0a47bda8dca17140474e4630d4d78fdf49da7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f50d22c4c3d6fe9f556f4aa51387fa6f8c4f5263e445f40a264f107e9cb63c4",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-07-06T04:38:12Z",
    "title_canon_sha256": "418220609271265a5786e22f01d2f08d42ab73544d83b33af0315d1b22c53546"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.04242",
    "kind": "arxiv",
    "version": 1
  }
}