Pith Number

pith:P2RU7AFO

pith:2026:P2RU7AFOEM7ZYZJ2ONEDHQYHH7

not attested not anchored not stored refs pending

Subgradient Methods on Manifolds with Lower Bounded Curvature

G. C. Bento, I. D. L. Melo, J. O. Lopes, J. X. Cruz Neto

arxiv:2605.24780 v1 · 2026-05-23 · 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{P2RU7AFOEM7ZYZJ2ONEDHQYHH7}

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	2026-05-26T01:03:57.793160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ea34f80ae233f9c653a734833c3073ffc6c24c33d9baa87ef5553a6404d3637

Aliases

arxiv: 2605.24780 · arxiv_version: 2605.24780v1 · doi: 10.48550/arxiv.2605.24780 · pith_short_12: P2RU7AFOEM7Z · pith_short_16: P2RU7AFOEM7ZYZJ2 · pith_short_8: P2RU7AFO

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/P2RU7AFOEM7ZYZJ2ONEDHQYHH7 \
  | 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: 7ea34f80ae233f9c653a734833c3073ffc6c24c33d9baa87ef5553a6404d3637

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bee0d8eabe076a063e91aaefee9b061e712bcf4b00041305f80f255b53223b39",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-23T23:45:37Z",
    "title_canon_sha256": "4f92f88170431e057ca1d5365be21d634572225a3aaab0119e708cec63578f3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.24780",
    "kind": "arxiv",
    "version": 1
  }
}