Pith Number

pith:X5DQEDGG

pith:2025:X5DQEDGG6RB2MIT2KKLASKZGZM

not attested not anchored not stored refs pending

Horospherically Convex Optimization on Hadamard Manifolds Part I: Analysis and Algorithms

Christopher Criscitiello, Jungbin Kim

arxiv:2505.16970 v1 · 2025-05-22 · math.OC · cs.NA · math.DG · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X5DQEDGG6RB2MIT2KKLASKZGZM}

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.

Cited by

1 paper in Pith

Minimal enclosing balls via geodesics

Receipt and verification

First computed	2026-07-05T11:07:43.875251Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf47020cc6f443a6227a5296092b26cb2a3ce36da264471f809b3284ea42cf10

Aliases

arxiv: 2505.16970 · arxiv_version: 2505.16970v1 · doi: 10.48550/arxiv.2505.16970 · pith_short_12: X5DQEDGG6RB2 · pith_short_16: X5DQEDGG6RB2MIT2 · pith_short_8: X5DQEDGG

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/X5DQEDGG6RB2MIT2KKLASKZGZM \
  | 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: bf47020cc6f443a6227a5296092b26cb2a3ce36da264471f809b3284ea42cf10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdc06bca7ae2b1ac3ac539eca0efe379d0f10ccb7b845c97ff03957c0b1b6a54",
    "cross_cats_sorted": [
      "cs.NA",
      "math.DG",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-05-22T17:50:10Z",
    "title_canon_sha256": "c370123cc1f3e2fefbc35036192a1e65ce85a1f908ffdaf1a10295fdb21b1850"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.16970",
    "kind": "arxiv",
    "version": 1
  }
}