Pith Number

pith:4QCTMV2E

pith:2026:4QCTMV2EPKM7RSV6KFM7WD4B73

not attested not anchored not stored refs pending

The horizontal Laplacian of a Riemannian submersion with totally geodesic fibers and an integrable horizontal distribution

Tatsuya Tate

arxiv:2606.17492 v1 · 2026-06-16 · 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{4QCTMV2EPKM7RSV6KFM7WD4B73}

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	2026-06-19T16:10:14.348520Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e4053657447a99f8cabe5159fb0f81feccd965bf349de78475006766f4a4306f

Aliases

arxiv: 2606.17492 · arxiv_version: 2606.17492v1 · doi: 10.48550/arxiv.2606.17492 · pith_short_12: 4QCTMV2EPKM7 · pith_short_16: 4QCTMV2EPKM7RSV6 · pith_short_8: 4QCTMV2E

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/4QCTMV2EPKM7RSV6KFM7WD4B73 \
  | 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: e4053657447a99f8cabe5159fb0f81feccd965bf349de78475006766f4a4306f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5222a7159963f7992577f612af0dd9832592b1a21c16c01d2e5e2de78179bb3",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-06-16T04:03:39Z",
    "title_canon_sha256": "53e4c12bd492f86e2d7d46795c6e791813dcb6dba625eb1fada321ce92fc7b7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17492",
    "kind": "arxiv",
    "version": 1
  }
}