Pith Number

pith:HYPWIQ7K

pith:2012:HYPWIQ7KVTPVWXJGVSS6SL6AU3

not attested not anchored not stored refs pending

On some applications of complex numbers to polar equations and cycloidal curves

A. Laradji, H. Azad, M. T. Mustafa

arxiv:1211.0178 v1 · 2012-10-30 · math.HO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HYPWIQ7KVTPVWXJGVSS6SL6AU3}

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	2026-05-18T03:41:42.834082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3e1f6443eaacdf5b5d26aca5e92fc0a6e633649b7cf1102ac89676e57f26765a

Aliases

arxiv: 1211.0178 · arxiv_version: 1211.0178v1 · doi: 10.48550/arxiv.1211.0178 · pith_short_12: HYPWIQ7KVTPV · pith_short_16: HYPWIQ7KVTPVWXJG · pith_short_8: HYPWIQ7K

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/HYPWIQ7KVTPVWXJGVSS6SL6AU3 \
  | 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: 3e1f6443eaacdf5b5d26aca5e92fc0a6e633649b7cf1102ac89676e57f26765a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "93b5a3f04f67dea18aa21ea5a1a1db3f47df1789031a5f859507a7c036b12daf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2012-10-30T23:16:03Z",
    "title_canon_sha256": "de54f63c8f57b319e69c5c6ef6f788bea0eba02dec154825e231c73a6f36cb42"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.0178",
    "kind": "arxiv",
    "version": 1
  }
}