Pith Number

pith:FU3SM42M

pith:2007:FU3SM42MT5Q3SWVI3DE7DVFNI2

not attested not anchored not stored refs pending

Knotted Topological Phase Singularities of Electromagnetic Field

Ji-rong Ren, Shu-Fan Mo, Tao Zhu

arxiv:0712.4198 v2 · 2007-12-27 · physics.optics · physics.class-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FU3SM42MT5Q3SWVI3DE7DVFNI2}

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	2026-05-18T02:16:02.493214Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d3726734c9f61b95aa8d8c9f1d4ad46be890c5cc81723fb624e7e16ffc98bd0

Aliases

arxiv: 0712.4198 · arxiv_version: 0712.4198v2 · doi: 10.48550/arxiv.0712.4198 · pith_short_12: FU3SM42MT5Q3 · pith_short_16: FU3SM42MT5Q3SWVI · pith_short_8: FU3SM42M

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/FU3SM42MT5Q3SWVI3DE7DVFNI2 \
  | 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: 2d3726734c9f61b95aa8d8c9f1d4ad46be890c5cc81723fb624e7e16ffc98bd0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "98d3ad34e6904bfdfa93cee09a4b35115974c19109a0aaf12fdd870b51b7c50a",
    "cross_cats_sorted": [
      "physics.class-ph"
    ],
    "license": "",
    "primary_cat": "physics.optics",
    "submitted_at": "2007-12-27T07:54:07Z",
    "title_canon_sha256": "1439900f8cd2b12e87f900fe4bbcb2286c6614e5cd4133802a1c1085683d9a4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.4198",
    "kind": "arxiv",
    "version": 2
  }
}