Pith Number

pith:YMGMPRB6

pith:2010:YMGMPRB6JL3VPYHLJ3GEASL6T2

not attested not anchored not stored refs pending

Conjugate Duality of Set--Valued Functions

Carola Schrage

arxiv:1012.4357 v5 · 2010-12-20 · 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{YMGMPRB6JL3VPYHLJ3GEASL6T2}

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	2026-05-18T02:50:52.217116Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c30cc7c43e4af757e0eb4ecc40497e9e851103946748d6667438f716a42f71fb

Aliases

arxiv: 1012.4357 · arxiv_version: 1012.4357v5 · doi: 10.48550/arxiv.1012.4357 · pith_short_12: YMGMPRB6JL3V · pith_short_16: YMGMPRB6JL3VPYHL · pith_short_8: YMGMPRB6

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/YMGMPRB6JL3VPYHLJ3GEASL6T2 \
  | 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: c30cc7c43e4af757e0eb4ecc40497e9e851103946748d6667438f716a42f71fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e4e5d14736f2a208920964effaad735a34c1081c5033bcd4e0c29e7866d66b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-12-20T15:29:23Z",
    "title_canon_sha256": "67294e2d62dbfb0370859bbf0af66e4481145210c0b9cc19c6109ae42334beef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4357",
    "kind": "arxiv",
    "version": 5
  }
}