Pith Number

pith:PB7A5Y3B

pith:2016:PB7A5Y3BIWN5OQXRIWJKOELJU5

not attested not anchored not stored refs pending

Algorithmic construction of the subdifferential from directional derivatives

Charles Audet, Warren Hare

arxiv:1609.02928 v1 · 2016-09-09 · 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{PB7A5Y3BIWN5OQXRIWJKOELJU5}

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	2026-05-18T01:04:49.344052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

787e0ee361459bd742f14592a71169a751f0176482963fb2faa8ed8f66f8b38c

Aliases

arxiv: 1609.02928 · arxiv_version: 1609.02928v1 · doi: 10.48550/arxiv.1609.02928 · pith_short_12: PB7A5Y3BIWN5 · pith_short_16: PB7A5Y3BIWN5OQXR · pith_short_8: PB7A5Y3B

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/PB7A5Y3BIWN5OQXRIWJKOELJU5 \
  | 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: 787e0ee361459bd742f14592a71169a751f0176482963fb2faa8ed8f66f8b38c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a46f32d6cf7be8e6bf38f717fa9f924c04ed68f60e53c2f2486ba816829757ef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-09-09T20:08:32Z",
    "title_canon_sha256": "266b6e50f223c0d523af9814531e4e3f84bca01945691e514211674faf6bdb00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.02928",
    "kind": "arxiv",
    "version": 1
  }
}