Pith Number

pith:MAWVCFKJ

pith:2015:MAWVCFKJ3WYEYAVZEUA3FFCMQG

not attested not anchored not stored refs pending

Diffraction-free beams in fractional Schr\"odinger equation

Hua Zhong, Milivoj R. Beli\'c, Min Xiao, Noor Ahmed, Yanpeng Zhang, Yiqi Zhang

arxiv:1512.08671 v3 · 2015-12-29 · 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{MAWVCFKJ3WYEYAVZEUA3FFCMQG}

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	2026-05-18T01:14:52.615623Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

602d511549ddb04c02b92501b2944c81856bac9056528d76da5ded907c5e80bb

Aliases

arxiv: 1512.08671 · arxiv_version: 1512.08671v3 · doi: 10.48550/arxiv.1512.08671 · pith_short_12: MAWVCFKJ3WYE · pith_short_16: MAWVCFKJ3WYEYAVZ · pith_short_8: MAWVCFKJ

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/MAWVCFKJ3WYEYAVZEUA3FFCMQG \
  | 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: 602d511549ddb04c02b92501b2944c81856bac9056528d76da5ded907c5e80bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3f9e9e9e4a9741c0e40d9fb9171eb461ac8aace13fcf79dac141711da9b4d82",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.optics",
    "submitted_at": "2015-12-29T12:55:51Z",
    "title_canon_sha256": "3ae0bd4af4a1dac26f7d228e71b2919558101eb9e849cf03ddc0b0a1939d3f13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08671",
    "kind": "arxiv",
    "version": 3
  }
}