Pith Number

pith:LZXMDR5G

pith:2011:LZXMDR5G4IJLAAZYLSELXKEK3R

not attested not anchored not stored refs pending

Fractional Trigonometric Functions in Complex-valued Space: Applications of Complex Number to Local Fractional Calculus of Complex Function

Xiao-Jun Yang

arxiv:1106.2783 v1 · 2011-06-14 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LZXMDR5G4IJLAAZYLSELXKEK3R}

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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	2026-05-18T04:10:08.663543Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e6ec1c7a6e212b003385c88bba88adc614ff0a19d33f40d706f5d207890f3c8

Aliases

arxiv: 1106.2783 · arxiv_version: 1106.2783v1 · doi: 10.48550/arxiv.1106.2783 · pith_short_12: LZXMDR5G4IJL · pith_short_16: LZXMDR5G4IJLAAZY · pith_short_8: LZXMDR5G

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/LZXMDR5G4IJLAAZYLSELXKEK3R \
  | 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: 5e6ec1c7a6e212b003385c88bba88adc614ff0a19d33f40d706f5d207890f3c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dee4288c01d0cc90b65d9c40650fa901ca6a3639788927113dae4e8151dbd592",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-06-14T18:34:38Z",
    "title_canon_sha256": "3f1da90db74086d430ea3f375aa48fef093c8dc11f5f1f2c58a1f69cd3ce1902"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.2783",
    "kind": "arxiv",
    "version": 1
  }
}