Pith Number

pith:E6Y4NQ23

pith:2024:E6Y4NQ23XYHVLH4AK2IFZL5CUT

not attested not anchored not stored refs pending

An Enhanced Levenberg--Marquardt Method via Gram Reduction

Chengchang Liu, John C.S. Lui, Luo Luo

arxiv:2412.08561 v1 · 2024-12-11 · 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{E6Y4NQ23XYHVLH4AK2IFZL5CUT}

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	2026-07-05T09:47:51.945833Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27b1c6c35bbe0f559f8056905cafa2a4c3ecc9b69d12b3260ed9cbeb48496390

Aliases

arxiv: 2412.08561 · arxiv_version: 2412.08561v1 · doi: 10.48550/arxiv.2412.08561 · pith_short_12: E6Y4NQ23XYHV · pith_short_16: E6Y4NQ23XYHVLH4A · pith_short_8: E6Y4NQ23

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/E6Y4NQ23XYHVLH4AK2IFZL5CUT \
  | 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: 27b1c6c35bbe0f559f8056905cafa2a4c3ecc9b69d12b3260ed9cbeb48496390

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a38b4013f85bdf242bb4530d6cf9b83ccb63d51f941df77de17ad55f4e9ebf7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2024-12-11T17:27:30Z",
    "title_canon_sha256": "41147bc572a1a68bbf46bae7b84a9af615b9898dd82102e67df4ccbecaa5d139"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.08561",
    "kind": "arxiv",
    "version": 1
  }
}