Pith Number

pith:4HX4OJOK

pith:2026:4HX4OJOKS2N6Z3MN7GUZSNF2HT

not attested not anchored not stored refs pending

Mean-Field Bose--Einstein Condensation and Condensate Ideals in the Resolvent Algebra

Yoshitsugu Sekine

arxiv:2607.02264 v1 · 2026-07-02 · math-ph · 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{4HX4OJOKS2N6Z3MN7GUZSNF2HT}

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	2026-07-03T01:17:46.935529Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1efc725ca969beced8df9a99934ba3cc816eeadc61f53af955085afa8159f7c

Aliases

arxiv: 2607.02264 · arxiv_version: 2607.02264v1 · doi: 10.48550/arxiv.2607.02264 · pith_short_12: 4HX4OJOKS2N6 · pith_short_16: 4HX4OJOKS2N6Z3MN · pith_short_8: 4HX4OJOK

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/4HX4OJOKS2N6Z3MN7GUZSNF2HT \
  | 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: e1efc725ca969beced8df9a99934ba3cc816eeadc61f53af955085afa8159f7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8a07606d2fb421f715b68a4e2a2a9626f647da901d7486165cceb91463331aa",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-07-02T14:51:05Z",
    "title_canon_sha256": "3c4ab77bffcd5eb18ebef1283df8e394f1c32c30e0d899514c75d00e04614fb3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.02264",
    "kind": "arxiv",
    "version": 1
  }
}