Pith Number

pith:4FR626F2

pith:2016:4FR626F2GWMRJV67WHJINNG4KQ

not attested not anchored not stored refs pending

A compact representation for minimizers of $k$-submodular functions

Hiroshi Hirai, Taihei Oki

arxiv:1610.00151 v2 · 2016-10-01 · 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{4FR626F2GWMRJV67WHJINNG4KQ}

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	2026-05-18T00:47:42.742113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e163ed78ba359914d7dfb1d286b4dc5434edcf3c4738848793d9eb26aef3d00a

Aliases

arxiv: 1610.00151 · arxiv_version: 1610.00151v2 · doi: 10.48550/arxiv.1610.00151 · pith_short_12: 4FR626F2GWMR · pith_short_16: 4FR626F2GWMRJV67 · pith_short_8: 4FR626F2

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/4FR626F2GWMRJV67WHJINNG4KQ \
  | 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: e163ed78ba359914d7dfb1d286b4dc5434edcf3c4738848793d9eb26aef3d00a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d171ff1e355478ed47c777dadc3b5a113462232ccc7a3657dac444c0fafc6089",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-10-01T15:42:16Z",
    "title_canon_sha256": "2ad3afaeed166e386f0161540bd1282342c504e51f39c3f09991f470584457f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.00151",
    "kind": "arxiv",
    "version": 2
  }
}