Pith Number

pith:R4WNAXYX

pith:2011:R4WNAXYXEUJSV7UKBOTOAEU3XR

not attested not anchored not stored refs pending

Polyharmonicity and algebraic support of measures

Hermann Render, Ognyan Kounchev

arxiv:1112.1511 v1 · 2011-12-07 · math.CV · math.FA · math.NA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R4WNAXYXEUJSV7UKBOTOAEU3XR}

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	2026-05-18T04:06:54.427027Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f2cd05f1725132afe8a0ba6e0129bbc7b7d82a9b4f4ac651acc835999573c0b

Aliases

arxiv: 1112.1511 · arxiv_version: 1112.1511v1 · doi: 10.48550/arxiv.1112.1511 · pith_short_12: R4WNAXYXEUJS · pith_short_16: R4WNAXYXEUJSV7UK · pith_short_8: R4WNAXYX

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/R4WNAXYXEUJSV7UKBOTOAEU3XR \
  | 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: 8f2cd05f1725132afe8a0ba6e0129bbc7b7d82a9b4f4ac651acc835999573c0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f1a70283723336761e2ce1a4fa20065f662791643ca0c3cbd3354f387675faa",
    "cross_cats_sorted": [
      "math.FA",
      "math.NA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2011-12-07T10:13:40Z",
    "title_canon_sha256": "2387eeba11dd2bb8a83bbdd7f3949313ad6d32f7342f97c2ac3fdcfd4d891b32"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1511",
    "kind": "arxiv",
    "version": 1
  }
}