Pith Number

pith:A2K5I7VH

pith:2026:A2K5I7VHCY4QDWGU2HVFPUD5VR

not attested not anchored not stored refs pending

A Residual-Shell-Based Lower Bound for Ollivier-Ricci Curvature

Huichun Zhang, Jian Sun, Xiang Gu

A residual-shell lower bound tightens estimates of Ollivier-Ricci curvature while remaining fast to compute.

arxiv:2604.12211 v2 · 2026-04-14 · cs.LG · cs.DS

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\usepackage{pith}
\pithnumber{A2K5I7VHCY4QDWGU2HVFPUD5VR}

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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.

Claims

C1strongest claim

We establish a substantially tighter lower bound for ORC than the existing lower bound, while retaining much lower computational cost than exact ORC computation, with practical speedups of tens of times. Moreover, our bound is not restricted to 1-hop random walks, but also applies to k-hop random walks (k > 1).

C2weakest assumption

The residual-shell correction term is assumed to preserve the lower-bound property for the Wasserstein distance without introducing additional looseness that would negate the claimed tightness gain; this is asserted but not derived in the abstract.

C3one line summary

A residual-shell construction yields a tighter, computationally cheap lower bound for Ollivier-Ricci curvature that works for both 1-hop and k-hop random walks.

Receipt and verification

First computed	2026-06-30T01:18:18.494092Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0695d47ea7163901d8d4d1ea57d07dac45ec275549c0cfa331a6d67e8c9e7792

Aliases

arxiv: 2604.12211 · arxiv_version: 2604.12211v2 · doi: 10.48550/arxiv.2604.12211 · pith_short_12: A2K5I7VHCY4Q · pith_short_16: A2K5I7VHCY4QDWGU · pith_short_8: A2K5I7VH

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/A2K5I7VHCY4QDWGU2HVFPUD5VR \
  | 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: 0695d47ea7163901d8d4d1ea57d07dac45ec275549c0cfa331a6d67e8c9e7792

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a84065899f9fd84267edcdf57756cfa292629e8933da1644499f8753025d79af",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-14T02:40:15Z",
    "title_canon_sha256": "d1330164dad2863671d971b72d491d5d3f212c49b2b799a78f324d091072fd65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.12211",
    "kind": "arxiv",
    "version": 2
  }
}