Pith Number

pith:OIQLO4FK

pith:2020:OIQLO4FKV6JLFO7SRHVKEBQJEX

not attested not anchored not stored refs pending

Constructing a subgradient from directional derivatives for functions of two variables

Kamil A. Khan, Yingwei Yuan

arxiv:2001.10670 v3 · 2020-01-29 · math.OC · cs.NA · math.NA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OIQLO4FKV6JLFO7SRHVKEBQJEX}

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	2026-07-05T06:23:29.037488Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7220b770aaaf92b2bbf289eaa2060925c06fe151b241db231a44911064714806

Aliases

arxiv: 2001.10670 · arxiv_version: 2001.10670v3 · doi: 10.48550/arxiv.2001.10670 · pith_short_12: OIQLO4FKV6JL · pith_short_16: OIQLO4FKV6JLFO7S · pith_short_8: OIQLO4FK

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/OIQLO4FKV6JLFO7SRHVKEBQJEX \
  | 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: 7220b770aaaf92b2bbf289eaa2060925c06fe151b241db231a44911064714806

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "260ff456fa8dd6d7fe515fbd5743c2f2f1dd7c3b7a61b6321050dfa08ddf50a0",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2020-01-29T02:42:30Z",
    "title_canon_sha256": "81d8fd8520d5457ded00e46142450e4235121d04ae6bf46ef94fe90d3eb38119"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.10670",
    "kind": "arxiv",
    "version": 3
  }
}