Pith Number

pith:L7KX2LMB

pith:2010:L7KX2LMB4F5GXPOZ3FK5KA2T3Y

not attested not anchored not stored refs pending

Duality for rectified Cost Functions

Aldo Pratelli, Mathias Beiglboeck

arxiv:1009.1825 v1 · 2010-09-09 · 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{L7KX2LMB4F5GXPOZ3FK5KA2T3Y}

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	2026-05-18T04:41:06.217922Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5fd57d2d81e17a6bbdd9d955d50353de34b843a0da94effd474180bd8c50a179

Aliases

arxiv: 1009.1825 · arxiv_version: 1009.1825v1 · doi: 10.48550/arxiv.1009.1825 · pith_short_12: L7KX2LMB4F5G · pith_short_16: L7KX2LMB4F5GXPOZ · pith_short_8: L7KX2LMB

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/L7KX2LMB4F5GXPOZ3FK5KA2T3Y \
  | 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: 5fd57d2d81e17a6bbdd9d955d50353de34b843a0da94effd474180bd8c50a179

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "99c79ebaa57f1861ae04ce5da5aea022a54efab3027026f34b5f6821463019d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-09-09T16:57:16Z",
    "title_canon_sha256": "6ba52d201a5e83bf6d2f4fdd67ec9b8b2b54c59c668cd2d72f22ee316332172a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.1825",
    "kind": "arxiv",
    "version": 1
  }
}