Pith Number

pith:JABT7JOJ

pith:2016:JABT7JOJBYEU3OWIBVPEDSDLZW

not attested not anchored not stored refs pending

Spherical Harmonics $Y_{l}^{m}(\theta,\phi)$: Positive and Negative Integer Representations of su(1,1) for l-m and l+m

H. Fakhri

arxiv:1602.07951 v1 · 2016-02-25 · 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{JABT7JOJBYEU3OWIBVPEDSDLZW}

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	2026-05-18T01:18:59.929878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48033fa5c90e094dbac80d5e41c86bcdb92b9d26572225a47d3c4a25eb68572e

Aliases

arxiv: 1602.07951 · arxiv_version: 1602.07951v1 · doi: 10.48550/arxiv.1602.07951 · pith_short_12: JABT7JOJBYEU · pith_short_16: JABT7JOJBYEU3OWI · pith_short_8: JABT7JOJ

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/JABT7JOJBYEU3OWIBVPEDSDLZW \
  | 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: 48033fa5c90e094dbac80d5e41c86bcdb92b9d26572225a47d3c4a25eb68572e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1923e28004d97c3f97c761a154fecee25e42a50af0ad227ffcab4391177f739",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2016-02-25T14:42:50Z",
    "title_canon_sha256": "d4dd1a4fbde788572cf5ec117a91b6dda471e6e8b064d4355428dd876c172079"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.07951",
    "kind": "arxiv",
    "version": 1
  }
}