Pith Number

pith:QO2C2J2J

pith:2012:QO2C2J2J5XT4N5ZSWEQRL7UQPG

not attested not anchored not stored refs pending

On the differentiability of directionally differentiable functions and applications

Hannes Luiro

arxiv:1208.3971 v2 · 2012-08-20 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QO2C2J2J5XT4N5ZSWEQRL7UQPG}

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	2026-05-18T03:26:08.801087Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83b42d2749ede7c6f732b12115fe907995fc5666fa6d69b0fa8e1bcc8438a6a8

Aliases

arxiv: 1208.3971 · arxiv_version: 1208.3971v2 · doi: 10.48550/arxiv.1208.3971 · pith_short_12: QO2C2J2J5XT4 · pith_short_16: QO2C2J2J5XT4N5ZS · pith_short_8: QO2C2J2J

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/QO2C2J2J5XT4N5ZSWEQRL7UQPG \
  | 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: 83b42d2749ede7c6f732b12115fe907995fc5666fa6d69b0fa8e1bcc8438a6a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "94e72497f8bf2a7fa48b32efe154aa8f6d9c1b8b3b078e251b2fb2962c19b5f0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-08-20T10:57:50Z",
    "title_canon_sha256": "e9d8b52aa9e555f817923c11262d2dceba7a1c06d269f481ae2ef168464c9f52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3971",
    "kind": "arxiv",
    "version": 2
  }
}