Pith Number

pith:HX7XA6LV

pith:2015:HX7XA6LVDLNGZ25YOSH4O2AATT

not attested not anchored not stored refs pending

Walk on Spheres Algorithm for Helmholtz and Yukawa Equations via Duffin Correspondence

Antti Rasila, Tommi Sottinen, Xuxin Yang

arxiv:1512.07725 v1 · 2015-12-24 · math.NA · math.AP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HX7XA6LVDLNGZ25YOSH4O2AATT}

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	2026-05-18T01:23:48.035496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3dff7079751ada6cebb8748fc768009ccd71881c7f18819a220015e706e3a345

Aliases

arxiv: 1512.07725 · arxiv_version: 1512.07725v1 · doi: 10.48550/arxiv.1512.07725 · pith_short_12: HX7XA6LVDLNG · pith_short_16: HX7XA6LVDLNGZ25Y · pith_short_8: HX7XA6LV

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/HX7XA6LVDLNGZ25YOSH4O2AATT \
  | 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: 3dff7079751ada6cebb8748fc768009ccd71881c7f18819a220015e706e3a345

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "241e9d9533671355ea936b5f24a2e2cdb8a1fc88aaea649915c91c0c6a87538a",
    "cross_cats_sorted": [
      "math.AP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2015-12-24T06:17:26Z",
    "title_canon_sha256": "b804ea7b6ecd8bfa95d26341dd5fd82457780a5751e8546d216ad2faa05e144f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07725",
    "kind": "arxiv",
    "version": 1
  }
}