Pith Number

pith:IUI52EGX

pith:2013:IUI52EGXKDTWJZQ3PRRUT4MDJB

not attested not anchored not stored refs pending

Properties of Hadamard directional derivatives: Denjoy-Young-Saks theorem for functions on Banach spaces

Ludek Zajicek

arxiv:1308.2415 v1 · 2013-08-11 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IUI52EGXKDTWJZQ3PRRUT4MDJB}

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	2026-05-18T03:16:07.498472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4511dd10d750e764e61b7c6349f1834868c327c04d358f24d206a0f61e15134e

Aliases

arxiv: 1308.2415 · arxiv_version: 1308.2415v1 · doi: 10.48550/arxiv.1308.2415 · pith_short_12: IUI52EGXKDTW · pith_short_16: IUI52EGXKDTWJZQ3 · pith_short_8: IUI52EGX

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/IUI52EGXKDTWJZQ3PRRUT4MDJB \
  | 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: 4511dd10d750e764e61b7c6349f1834868c327c04d358f24d206a0f61e15134e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eca6c7691429fae36a8ed6f2154ade19ea21476d3aef7c3ae3490338336cc02b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-08-11T18:25:23Z",
    "title_canon_sha256": "0fadbc8c539af727223b4b2fadff886aed39223741903e5f6a3633c52fc10e83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2415",
    "kind": "arxiv",
    "version": 1
  }
}