Pith Number

pith:6APWI4UF

pith:2019:6APWI4UFZLWWCP6OORDKEMCW5B

not attested not anchored not stored refs pending

Mean value properties of harmonic functions and related topics (a survey)

Nikolay Kuznetsov

arxiv:1904.08312 v2 · 2019-04-15 · math.AP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6APWI4UFZLWWCP6OORDKEMCW5B}

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	2026-05-17T23:45:22.269090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f01f647285caed613fce7446a23056e86ef125f9073d13e1044cd91f4127b63c

Aliases

arxiv: 1904.08312 · arxiv_version: 1904.08312v2 · doi: 10.48550/arxiv.1904.08312 · pith_short_12: 6APWI4UFZLWW · pith_short_16: 6APWI4UFZLWWCP6O · pith_short_8: 6APWI4UF

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/6APWI4UFZLWWCP6OORDKEMCW5B \
  | 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: f01f647285caed613fce7446a23056e86ef125f9073d13e1044cd91f4127b63c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10d1226941eeb06c828cf1773bc108ddefa2f30eef83df13bf27c56966da4bdc",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-04-15T18:04:38Z",
    "title_canon_sha256": "69434099c8f2e226e2a51f83cd9fb9a528a580e15dd8a6be5fc8cc94ec92093a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.08312",
    "kind": "arxiv",
    "version": 2
  }
}