Pith Number

pith:VZXN6QVO

pith:2011:VZXN6QVOABVHTPD5AM6KFW2XJZ

not attested not anchored not stored refs pending

Separately twice differentiable functions and the equation of string oscillation

Taras Banakh, Volodymyr Mykhaylyuk

arxiv:1104.5211 v1 · 2011-04-27 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VZXN6QVOABVHTPD5AM6KFW2XJZ}

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	2026-05-18T03:38:14.531328Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae6edf42ae006a79bc7d033ca2db574e50afd1122cf8ed31d2f4ca088f72b913

Aliases

arxiv: 1104.5211 · arxiv_version: 1104.5211v1 · doi: 10.48550/arxiv.1104.5211 · pith_short_12: VZXN6QVOABVH · pith_short_16: VZXN6QVOABVHTPD5 · pith_short_8: VZXN6QVO

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/VZXN6QVOABVHTPD5AM6KFW2XJZ \
  | 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: ae6edf42ae006a79bc7d033ca2db574e50afd1122cf8ed31d2f4ca088f72b913

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a807d2f43752b24972cc6e210613f2ea9e4b379e4aca784bb7bddc3d31361613",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-04-27T18:35:28Z",
    "title_canon_sha256": "c64273f534fdcbfeec7a9311051964db4b16d3e556903d802c2e98ac8d25793a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.5211",
    "kind": "arxiv",
    "version": 1
  }
}