Pith Number

pith:DJTRQ7LH

pith:2025:DJTRQ7LH4EEE2AOBFNBEGD4X55

not attested not anchored not stored refs pending

Duality between polyhedral approximation of value functions and optimal quantization of measures

Abdellah Bulaich Mehamdi, Luce Brotcorne, Quentin Jacquet, St\'ephane Gaubert, Wim van Ackooij

arxiv:2509.04101 v1 · 2025-09-04 · 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{DJTRQ7LH4EEE2AOBFNBEGD4X55}

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	2026-07-05T12:04:53.495471Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a67187d67e1084d01c12b42430f97ef7cc586220b0bf2fa80a25c3556d188e1

Aliases

arxiv: 2509.04101 · arxiv_version: 2509.04101v1 · doi: 10.48550/arxiv.2509.04101 · pith_short_12: DJTRQ7LH4EEE · pith_short_16: DJTRQ7LH4EEE2AOB · pith_short_8: DJTRQ7LH

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/DJTRQ7LH4EEE2AOBFNBEGD4X55 \
  | 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: 1a67187d67e1084d01c12b42430f97ef7cc586220b0bf2fa80a25c3556d188e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6052a03a076b0e201301e2b69cb6128cf3e48b773362123ebb451c68eb3a9aab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-09-04T11:04:10Z",
    "title_canon_sha256": "e96e25049e42a8ee65440cddd433b7d64bdfebf423d531fa6e5b7ad63b91c18f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.04101",
    "kind": "arxiv",
    "version": 1
  }
}