Pith Number

pith:TAWXNKKX

pith:2015:TAWXNKKXNBPAWN26YN6U2ZL4H7

not attested not anchored not stored refs pending

Ab initio derivation of multipolar expansion of optical force

Jack Ng, Yikun Jiang, Zhifang Lin

arxiv:1512.04201 v3 · 2015-12-14 · physics.optics

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TAWXNKKXNBPAWN26YN6U2ZL4H7}

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	2026-05-18T00:26:02.414547Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

982d76a957685e0b375ec37d4d657c3fc5504cb8d41fdefb940a8c1cf7cca0ea

Aliases

arxiv: 1512.04201 · arxiv_version: 1512.04201v3 · doi: 10.48550/arxiv.1512.04201 · pith_short_12: TAWXNKKXNBPA · pith_short_16: TAWXNKKXNBPAWN26 · pith_short_8: TAWXNKKX

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/TAWXNKKXNBPAWN26YN6U2ZL4H7 \
  | 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: 982d76a957685e0b375ec37d4d657c3fc5504cb8d41fdefb940a8c1cf7cca0ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f80ee02be6cd3cb2fc101d0b39c13310637936ba830606b79ecb50b8282d98e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2015-12-14T07:11:53Z",
    "title_canon_sha256": "93056ed061e23461e2a1495fc366af2d141fabfcef62c3a7324a32f67d2f72e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04201",
    "kind": "arxiv",
    "version": 3
  }
}