Pith Number

pith:SYMA54QI

pith:2012:SYMA54QIXNREMEQBRGCFOQ5CB2

not attested not anchored not stored refs pending

Directed Subdifferentiable Functions and the Directed Subdifferential without Delta-Convex Structure

Elza Farkhi, Robert Baier, Vera Roshchina

arxiv:1212.1508 v2 · 2012-12-07 · 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{SYMA54QIXNREMEQBRGCFOQ5CB2}

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	2026-05-18T01:37:21.920402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

96180ef208bb6246120189845743a20eb969fe906350553df432bf0858677774

Aliases

arxiv: 1212.1508 · arxiv_version: 1212.1508v2 · doi: 10.48550/arxiv.1212.1508 · pith_short_12: SYMA54QIXNRE · pith_short_16: SYMA54QIXNREMEQB · pith_short_8: SYMA54QI

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/SYMA54QIXNREMEQBRGCFOQ5CB2 \
  | 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: 96180ef208bb6246120189845743a20eb969fe906350553df432bf0858677774

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec5062a9b62d462c10faeb2e81ba9132ce34c58c33a76550624a3ec6a518abc1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-12-07T00:18:38Z",
    "title_canon_sha256": "956f738606021613ab9a1db494b74fc2fde3cab4f77fa8ba1585e26db9366462"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.1508",
    "kind": "arxiv",
    "version": 2
  }
}