Pith Number

pith:AKMHX5PP

pith:2025:AKMHX5PPA2R576U2K5QAKSVZIA

not attested not anchored not stored refs pending

Generalized Twice Differentiability and Quadratic Bundles in Second-Order Variational Analysis

Boris S. Mordukhovich, Le Duc Viet, Pham Duy Khanh, Vo Thanh Phat

arxiv:2501.02067 v1 · 2025-01-03 · 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{AKMHX5PPA2R576U2K5QAKSVZIA}

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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.

Cited by

1 paper in Pith

Characterizations of Variational Convexity and Tilt Stability via Quadratic Bundles

Receipt and verification

First computed	2026-07-05T09:57:01.636849Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02987bf5ef06a3dffa9a5760054ab94009d817b77d52798543b005abe4f464a0

Aliases

arxiv: 2501.02067 · arxiv_version: 2501.02067v1 · doi: 10.48550/arxiv.2501.02067 · pith_short_12: AKMHX5PPA2R5 · pith_short_16: AKMHX5PPA2R576U2 · pith_short_8: AKMHX5PP

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/AKMHX5PPA2R576U2K5QAKSVZIA \
  | 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: 02987bf5ef06a3dffa9a5760054ab94009d817b77d52798543b005abe4f464a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e85be2554f25cfc5c6d67e1357292dade5384766e2b6aa52e996cd6c44fd9a2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-01-03T19:20:23Z",
    "title_canon_sha256": "89d671664a6db24e543cdc0ef81fdcf3df295beae5165126861147d6e6cd4d87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.02067",
    "kind": "arxiv",
    "version": 1
  }
}