Pith Number

pith:SC7EB3IY

pith:2021:SC7EB3IY5ZOCPUVRD3AZVNQ6UX

not attested not anchored not stored refs pending

Fenchel-Rockafellar Theorem in Infinite Dimensions via Generalized Relative Interiors

Boris Mordukhovich, Dang Van Cuong, Gary Sandine, Nguyen Mau Nam

arxiv:2104.13510 v3 · 2021-04-27 · math.FA · 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{SC7EB3IY5ZOCPUVRD3AZVNQ6UX}

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	2026-07-05T05:54:25.903854Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

90be40ed18ee5c27d2b11ec19ab61ea5e0eb87a1b1914d46830583ee3990f80e

Aliases

arxiv: 2104.13510 · arxiv_version: 2104.13510v3 · doi: 10.48550/arxiv.2104.13510 · pith_short_12: SC7EB3IY5ZOC · pith_short_16: SC7EB3IY5ZOCPUVR · pith_short_8: SC7EB3IY

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/SC7EB3IY5ZOCPUVRD3AZVNQ6UX \
  | 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: 90be40ed18ee5c27d2b11ec19ab61ea5e0eb87a1b1914d46830583ee3990f80e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4180577bbfc3f9c83c19035965b70c76b67e4f27aefb82b1a3b4e47953969525",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2021-04-27T23:55:02Z",
    "title_canon_sha256": "33807d0c8d9cd897ad0458baecb4b2323abb5a08759b5b013d3504c203875744"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.13510",
    "kind": "arxiv",
    "version": 3
  }
}