Pith Number

pith:VPXWNJ5I

pith:2010:VPXWNJ5IAWVQELN4OP4VRH4CEL

not attested not anchored not stored refs pending

The Bogoliubov inequality and the nature of Bose-Einstein condensates for interacting atoms in spatial dimensions $D \le 2$

Moorad Alexanian

arxiv:1009.3302 v2 · 2010-09-17 · cond-mat.quant-gas

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VPXWNJ5IAWVQELN4OP4VRH4CEL}

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	2026-05-17T23:39:32.838514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abef66a7a805ab022dbc73f9589f8222c244e9f282179812fccd6abbd36f3c90

Aliases

arxiv: 1009.3302 · arxiv_version: 1009.3302v2 · doi: 10.48550/arxiv.1009.3302 · pith_short_12: VPXWNJ5IAWVQ · pith_short_16: VPXWNJ5IAWVQELN4 · pith_short_8: VPXWNJ5I

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/VPXWNJ5IAWVQELN4OP4VRH4CEL \
  | 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: abef66a7a805ab022dbc73f9589f8222c244e9f282179812fccd6abbd36f3c90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0e931f80efcd1a2754f6a765dfb0e8679a107c5c4e76924a04202cfd93077a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.quant-gas",
    "submitted_at": "2010-09-17T00:24:02Z",
    "title_canon_sha256": "58b77df92a49c45eb6c0ec82ab57070820629e012ed291e754a062c49036a011"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3302",
    "kind": "arxiv",
    "version": 2
  }
}