Pith Number

pith:IOQTP6CP

pith:2018:IOQTP6CPJ6ANRYJ6CCTXKP6WYO

not attested not anchored not stored refs pending

Subdifferential formulae for the supremum of an arbitrary family of functions

Pedro P\'erez-Aros

arxiv:1801.00724 v2 · 2018-01-02 · 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{IOQTP6CPJ6ANRYJ6CCTXKP6WYO}

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	2026-05-17T23:59:17.770271Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

43a137f84f4f80d8e13e10a7753fd6c3ada0bd017493d165d668d10e11a9bcba

Aliases

arxiv: 1801.00724 · arxiv_version: 1801.00724v2 · doi: 10.48550/arxiv.1801.00724 · pith_short_12: IOQTP6CPJ6AN · pith_short_16: IOQTP6CPJ6ANRYJ6 · pith_short_8: IOQTP6CP

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/IOQTP6CPJ6ANRYJ6CCTXKP6WYO \
  | 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: 43a137f84f4f80d8e13e10a7753fd6c3ada0bd017493d165d668d10e11a9bcba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "235c0dcd5d972dd071ce1cf1a569a9f231275d483678cf5e037a1d1a3ac5e02d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-01-02T16:57:28Z",
    "title_canon_sha256": "f2816e3786b7c477fc3cdca41a7ea723aab85a7ee7d5da80cd349d344add46db"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.00724",
    "kind": "arxiv",
    "version": 2
  }
}