Pith Number

pith:5UTZWJ4I

pith:2016:5UTZWJ4I6QFBN77XEWKPFGQ534

not attested not anchored not stored refs pending

Gradient walk and $p$-harmonic functions

Hannes Luiro, Mikko Parviainen

arxiv:1605.05564 v1 · 2016-05-18 · 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{5UTZWJ4I6QFBN77XEWKPFGQ534}

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	2026-05-18T01:14:34.572006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ed279b2788f40a16fff72594f29a1ddf04382f22336a7a4f806ff4cc77dd0b29

Aliases

arxiv: 1605.05564 · arxiv_version: 1605.05564v1 · doi: 10.48550/arxiv.1605.05564 · pith_short_12: 5UTZWJ4I6QFB · pith_short_16: 5UTZWJ4I6QFBN77X · pith_short_8: 5UTZWJ4I

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/5UTZWJ4I6QFBN77XEWKPFGQ534 \
  | 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: ed279b2788f40a16fff72594f29a1ddf04382f22336a7a4f806ff4cc77dd0b29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "137e14b1ba8559dc9faf3d900a853e71920c14d3f2c509804d034bf812cf99eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-05-18T12:59:11Z",
    "title_canon_sha256": "d1d75fed76fee12c75142e44f5819a96a60ace30496f713b857fa6caa2cee926"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.05564",
    "kind": "arxiv",
    "version": 1
  }
}