Pith Number

pith:HTPSTKDX

pith:2016:HTPSTKDXINO6W4GRSM3LVUIMTC

not attested not anchored not stored refs pending

The virial theorem and ground state energy estimate of nonlinear Schr\"odinger equations in $\mathbb{R}^2$ with square root and saturable nonlinearities in nonlinear optics

Goong Chen, Hichem Hajaiej, Milan S. Petrovic, Milivoj R. Belic, Tai-Chia Lin

arxiv:1608.06102 v1 · 2016-08-22 · math.AP · math-ph · math.MP · nlin.PS · 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{HTPSTKDXINO6W4GRSM3LVUIMTC}

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	2026-05-18T01:08:22.278222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3cdf29a877435deb70d19336bad10c9890e2b344da6f0ff9c0ee5eac5bbc3d28

Aliases

arxiv: 1608.06102 · arxiv_version: 1608.06102v1 · doi: 10.48550/arxiv.1608.06102 · pith_short_12: HTPSTKDXINO6 · pith_short_16: HTPSTKDXINO6W4GR · pith_short_8: HTPSTKDX

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/HTPSTKDXINO6W4GRSM3LVUIMTC \
  | 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: 3cdf29a877435deb70d19336bad10c9890e2b344da6f0ff9c0ee5eac5bbc3d28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ca1720590af0bab59deb8c97a895d6944450546d5fc6e21b6099cea0cbceac1",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "nlin.PS",
      "physics.optics"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-08-22T09:53:41Z",
    "title_canon_sha256": "84d71513baab1ee6d981c517b22bf5b5c8e7f8aa3f9c9be9fdd9993ee9ece2ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.06102",
    "kind": "arxiv",
    "version": 1
  }
}