Pith Number

pith:TDFE7YW4

pith:2013:TDFE7YW4S5JAHLR3TCHZNFAZL4

not attested not anchored not stored refs pending

Second-order growth, tilt stability, and metric regularity of the subdifferential

B.S. Mordukhovich, D. Drusvyatskiy, T.T.A. Nghia

arxiv:1304.7385 v1 · 2013-04-27 · 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{TDFE7YW4S5JAHLR3TCHZNFAZL4}

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	2026-05-18T03:26:54.176679Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

98ca4fe2dc975203ae3b988f9694195f0b72d73a0b493033d228dfc2dc3c1b5f

Aliases

arxiv: 1304.7385 · arxiv_version: 1304.7385v1 · doi: 10.48550/arxiv.1304.7385 · pith_short_12: TDFE7YW4S5JA · pith_short_16: TDFE7YW4S5JAHLR3 · pith_short_8: TDFE7YW4

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/TDFE7YW4S5JAHLR3TCHZNFAZL4 \
  | 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: 98ca4fe2dc975203ae3b988f9694195f0b72d73a0b493033d228dfc2dc3c1b5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4f7e1e7f6386feee7756c7e4d140f51835509a51ca396035f7448900300c98e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2013-04-27T16:10:51Z",
    "title_canon_sha256": "66281614b6be11c56f02dcd5c8510f5adaf12246e6a78b52abf8d328ed9cc5de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.7385",
    "kind": "arxiv",
    "version": 1
  }
}