Pith Number

pith:T6332HFS

pith:2026:T6332HFS423H472BIXDAVL2NE7

not attested not anchored not stored refs pending

The Blessing and Curse of Curvature in Higher-Order Optimization: Horospherical versus Geodesic Convexity

Andi Han

arxiv:2608.06719 v1 · 2026-08-07 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{T6332HFS423H472BIXDAVL2NE7}

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	2026-08-10T01:11:48.809977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9fb7bd1cb2e6b67e7f4145c60aaf4d27f7d4eae73759187a85b74ff6058a421a

Aliases

arxiv: 2608.06719 · arxiv_version: 2608.06719v1 · doi: 10.48550/arxiv.2608.06719 · pith_short_12: T6332HFS423H · pith_short_16: T6332HFS423H472B · pith_short_8: T6332HFS

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/T6332HFS423H472BIXDAVL2NE7 \
  | 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: 9fb7bd1cb2e6b67e7f4145c60aaf4d27f7d4eae73759187a85b74ff6058a421a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff31f9ab31bdc950613b7fc22dc4c0a4db058a7ab0dd84140834003a4749afa1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-08-07T02:27:02Z",
    "title_canon_sha256": "3cae7b8ce3b1a3641db3199da2f2899b442590dc24bfe6e6508c32424440656a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.06719",
    "kind": "arxiv",
    "version": 1
  }
}