Pith Number

pith:NKCGKISS

pith:2017:NKCGKISSXXO4IXMQQL3ET4GFQW

not attested not anchored not stored refs pending

Formulae for the Conjugate and the Subdifferential of the Supremum Function

Pedro P\'erez-Aros

arxiv:1712.09318 v2 · 2017-12-26 · 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{NKCGKISSXXO4IXMQQL3ET4GFQW}

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	2026-05-18T00:14:59.644960Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a84652252bdddc45d9082f649f0c585a27ad304d00d2342bd5750daf4aaa397

Aliases

arxiv: 1712.09318 · arxiv_version: 1712.09318v2 · doi: 10.48550/arxiv.1712.09318 · pith_short_12: NKCGKISSXXO4 · pith_short_16: NKCGKISSXXO4IXMQ · pith_short_8: NKCGKISS

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/NKCGKISSXXO4IXMQQL3ET4GFQW \
  | 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: 6a84652252bdddc45d9082f649f0c585a27ad304d00d2342bd5750daf4aaa397

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a49b0fe6d6fe92394aea39f47b2d08f49c5a038463388df1c7c36b5aaa3d45aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2017-12-26T18:07:38Z",
    "title_canon_sha256": "943f667d54887ef4535b098cee5032fd35f9b212a5aea26d50602372edcb3651"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.09318",
    "kind": "arxiv",
    "version": 2
  }
}