Pith Number

pith:27TEQYES

pith:2015:27TEQYESSK56HCKPZMA3C6C2W2

not attested not anchored not stored refs pending

Bogoliubov correction to the mean-field dynamics of interacting bosons

Marcin Napi\'orkowski, Phan Th\`anh Nam

arxiv:1509.04631 v3 · 2015-09-15 · math-ph · math.AP · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{27TEQYESSK56HCKPZMA3C6C2W2}

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	2026-05-18T00:36:41.614642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7e648609292bbe3894fcb01b1785ab6b3b109d6b0f2e1edfdc8228a2bfa1e28

Aliases

arxiv: 1509.04631 · arxiv_version: 1509.04631v3 · doi: 10.48550/arxiv.1509.04631 · pith_short_12: 27TEQYESSK56 · pith_short_16: 27TEQYESSK56HCKP · pith_short_8: 27TEQYES

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/27TEQYESSK56HCKPZMA3C6C2W2 \
  | 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: d7e648609292bbe3894fcb01b1785ab6b3b109d6b0f2e1edfdc8228a2bfa1e28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "882d25d00fa53c4348cdb03adf45f84528894e2e1761a4caab707b0d20aaa304",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-09-15T16:31:53Z",
    "title_canon_sha256": "69c478414e49cef33ad0ee9718577e79a61fd5f7ef41f2521640a2e43c6e9fa3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.04631",
    "kind": "arxiv",
    "version": 3
  }
}