Pith Number

pith:UKD7OKDA

pith:2018:UKD7OKDA6S6H7ELDCRID4NBGGX

not attested not anchored not stored refs pending

Extensions of convex functions with prescribed subdifferentials

Carlos Mudarra, Daniel Azagra, Javier G\'omez-Gil, Juan Ferrera

arxiv:1811.05538 v2 · 2018-11-13 · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UKD7OKDA6S6H7ELDCRID4NBGGX}

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	2026-05-17T23:48:22.277059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a287f72860f4bc7f916314503e342635deeb7d62c625e5dca294d21989fd184d

Aliases

arxiv: 1811.05538 · arxiv_version: 1811.05538v2 · doi: 10.48550/arxiv.1811.05538 · pith_short_12: UKD7OKDA6S6H · pith_short_16: UKD7OKDA6S6H7ELD · pith_short_8: UKD7OKDA

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/UKD7OKDA6S6H7ELDCRID4NBGGX \
  | 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: a287f72860f4bc7f916314503e342635deeb7d62c625e5dca294d21989fd184d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4addba32f7a3616b42a79c81444a4ce51cbd940ec6167568671170dd3356b12e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-11-13T21:52:53Z",
    "title_canon_sha256": "50cc447f9f2b9ebe3897bd3786fafad6c532de7b36583cd03f21727b986c66bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.05538",
    "kind": "arxiv",
    "version": 2
  }
}