Pith Number

pith:VDZBMGIN

pith:2018:VDZBMGINRATDQYRILDRP43YYJR

not attested not anchored not stored refs pending

Laser Mode Bifurcations Induced by $\mathcal{PT}$-Breaking Exceptional Points

B. F. Zhu, Q. J. Wang, Y. D. Chong

arxiv:1812.01872 v1 · 2018-12-05 · physics.optics

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDZBMGINRATDQYRILDRP43YYJR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-17T23:50:09.382109Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8f216190d882638622858e2fe6f184c6884332d88cd978f8e54052f58e69424

Aliases

arxiv: 1812.01872 · arxiv_version: 1812.01872v1 · doi: 10.48550/arxiv.1812.01872 · pith_short_12: VDZBMGINRATD · pith_short_16: VDZBMGINRATDQYRI · pith_short_8: VDZBMGIN

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/VDZBMGINRATDQYRILDRP43YYJR \
  | 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: a8f216190d882638622858e2fe6f184c6884332d88cd978f8e54052f58e69424

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a16c8bb85fea878ae1ce6f5aca4ff9666cb5b876a52ca2c48972952721a8492e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2018-12-05T09:39:13Z",
    "title_canon_sha256": "981dbe6b8af61f63e1ba1fa11e3785e4fd8950f22bc7adafb28deee6a8a9033b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.01872",
    "kind": "arxiv",
    "version": 1
  }
}