Pith Number

pith:5GZKTMLB

pith:2015:5GZKTMLBLZ3GKJVVLSQQEBNMJH

not attested not anchored not stored refs pending

A Liouville property for gradient graphs and a Bernstein problem for Hamiltonian stationary equations

Micah Warren

arxiv:1505.04152 v1 · 2015-05-15 · 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{5GZKTMLBLZ3GKJVVLSQQEBNMJH}

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	2026-05-18T02:09:39.923954Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9b2a9b1615e766526b55ca10205ac49cd730d9b37af798ca1a05c122fd18d0f

Aliases

arxiv: 1505.04152 · arxiv_version: 1505.04152v1 · doi: 10.48550/arxiv.1505.04152 · pith_short_12: 5GZKTMLBLZ3G · pith_short_16: 5GZKTMLBLZ3GKJVV · pith_short_8: 5GZKTMLB

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/5GZKTMLBLZ3GKJVVLSQQEBNMJH \
  | 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: e9b2a9b1615e766526b55ca10205ac49cd730d9b37af798ca1a05c122fd18d0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b5c170c6c05dc44b29524d8a8d8bd6cb4b5a5ab3db144b43e8b2667cb6a6cdcc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-05-15T18:42:51Z",
    "title_canon_sha256": "2d934491414075cdef6b095c795cda4ab6e1051a1771992f912bf20abb0e7668"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04152",
    "kind": "arxiv",
    "version": 1
  }
}