Pith Number

pith:HLHPY3WA

pith:2011:HLHPY3WAW5PJHLB7IRGM4APPSV

not attested not anchored not stored refs pending

On the meaning of the Vakhitov-Kolokolov stability criterion for the nonlinear Dirac equation

Andrew Comech

arxiv:1107.1763 v2 · 2011-07-09 · math.AP · hep-th · math-ph · math.MP · nlin.PS

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\usepackage{pith}
\pithnumber{HLHPY3WAW5PJHLB7IRGM4APPSV}

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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.

Cited by

1 paper in Pith

Generalized PT-symmetric nonlinear Dirac equation: exact solitary waves solutions, stability and conservation laws

Receipt and verification

First computed	2026-05-18T04:15:35.850616Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3acefc6ec0b75e93ac3f444cce01ef95445bb1536f55b569b3fb39c8cda4915a

Aliases

arxiv: 1107.1763 · arxiv_version: 1107.1763v2 · doi: 10.48550/arxiv.1107.1763 · pith_short_12: HLHPY3WAW5PJ · pith_short_16: HLHPY3WAW5PJHLB7 · pith_short_8: HLHPY3WA

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/HLHPY3WAW5PJHLB7IRGM4APPSV \
  | 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: 3acefc6ec0b75e93ac3f444cce01ef95445bb1536f55b569b3fb39c8cda4915a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17bc2fd84208084d462aed5cc14132d9ef02a2962ed9dd1e70d3c6902b92e072",
    "cross_cats_sorted": [
      "hep-th",
      "math-ph",
      "math.MP",
      "nlin.PS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-07-09T06:48:00Z",
    "title_canon_sha256": "543480b25f0127a5d4d3f4f1655cb289802b219d39c427689b087cea92efa58a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.1763",
    "kind": "arxiv",
    "version": 2
  }
}