Pith Number

pith:D7CLRNNM

pith:2015:D7CLRNNMQII4QHBLVIFRAK4AZU

not attested not anchored not stored refs pending

Stability of saddle points via explicit coderivatives of pointwise subdifferentials

Christian Clason, Tuomo Valkonen

arxiv:1509.06582 v3 · 2015-09-22 · 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{D7CLRNNMQII4QHBLVIFRAK4AZU}

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	2026-05-18T00:51:01.460214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fc4b8b5ac8211c81c2baa0b102b80cd05c165a0d280c5e2a90b22a9728bddfa

Aliases

arxiv: 1509.06582 · arxiv_version: 1509.06582v3 · doi: 10.48550/arxiv.1509.06582 · pith_short_12: D7CLRNNMQII4 · pith_short_16: D7CLRNNMQII4QHBL · pith_short_8: D7CLRNNM

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/D7CLRNNMQII4QHBLVIFRAK4AZU \
  | 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: 1fc4b8b5ac8211c81c2baa0b102b80cd05c165a0d280c5e2a90b22a9728bddfa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35b71eb9fd19eddae393b90d36163da307e9360ac7cf64088c4c4661ec5e4c9c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2015-09-22T12:59:57Z",
    "title_canon_sha256": "f5c865fe593d5d0d2653f4e15dca35240e57b9dcf14567ab255f2673bf793ad1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06582",
    "kind": "arxiv",
    "version": 3
  }
}