Pith Number

pith:LKCYZ34G

pith:2017:LKCYZ34GL2EBUCVS75EJ4CZBRN

not attested not anchored not stored refs pending

Calculus for directional limiting normal cones and subdifferentials

Helmut Gfrerer, Ji\v{r}\'i V. Outrata, Mat\'u\v{s} Benko

arxiv:1712.04704 v1 · 2017-12-13 · 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{LKCYZ34GL2EBUCVS75EJ4CZBRN}

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	2026-05-18T00:28:03.658163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a858cef865e881a0ab2ff489e0b218b622816aeea4e92aa1b6cd049f4e955a8

Aliases

arxiv: 1712.04704 · arxiv_version: 1712.04704v1 · doi: 10.48550/arxiv.1712.04704 · pith_short_12: LKCYZ34GL2EB · pith_short_16: LKCYZ34GL2EBUCVS · pith_short_8: LKCYZ34G

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/LKCYZ34GL2EBUCVS75EJ4CZBRN \
  | 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: 5a858cef865e881a0ab2ff489e0b218b622816aeea4e92aa1b6cd049f4e955a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4edb7455429d95e4cbd8275ccf335f9c15efe06ab028bd2090db2b76e69987a4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2017-12-13T11:04:16Z",
    "title_canon_sha256": "c7f10ea4dad20ae1986d12e00a73fa46a91eeeaf25102b299c856d7081ffb35f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.04704",
    "kind": "arxiv",
    "version": 1
  }
}