Pith Number

pith:5YQCTAK4

pith:2018:5YQCTAK4CEYYQ44EFUHBVVJ4RR

not attested not anchored not stored refs pending

Harmonic maps and biharmonic Riemanian submersions

Hajime Urakawa

arxiv:1809.10814 v1 · 2018-09-28 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5YQCTAK4CEYYQ44EFUHBVVJ4RR}

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	2026-05-18T00:04:34.969446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee2029815c11318873842d0e1ad53c8c70d60c22184931562ff48f9be2aed356

Aliases

arxiv: 1809.10814 · arxiv_version: 1809.10814v1 · doi: 10.48550/arxiv.1809.10814 · pith_short_12: 5YQCTAK4CEYY · pith_short_16: 5YQCTAK4CEYYQ44E · pith_short_8: 5YQCTAK4

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/5YQCTAK4CEYYQ44EFUHBVVJ4RR \
  | 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: ee2029815c11318873842d0e1ad53c8c70d60c22184931562ff48f9be2aed356

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "baf857483b541494778ed83e29b78f32fcda4dc71f86b5f6f7388a0f5dc5acc1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-09-28T01:31:49Z",
    "title_canon_sha256": "730311f55c9614446c441c0779fc02ecc16d1b50fdd89830feba355e1a9b35ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.10814",
    "kind": "arxiv",
    "version": 1
  }
}