Pith Number

pith:E3N67DRM

pith:2026:E3N67DRMXZSH5EZJTTVS257KRR

not attested not anchored not stored refs pending

Proper condensates and the Onsager-Penrose condition: A friendly debate on Bose-Einstein condensation

Detlev Buchholz

arxiv:2608.13402 v1 · 2026-08-13 · 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{E3N67DRMXZSH5EZJTTVS257KRR}

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	2026-08-14T01:04:22.140004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26dbef8e2cbe647e93299ceb2d77ea8c79feed1db97f8d73580e0eb2dd5db8a2

Aliases

arxiv: 2608.13402 · arxiv_version: 2608.13402v1 · doi: 10.48550/arxiv.2608.13402 · pith_short_12: E3N67DRMXZSH · pith_short_16: E3N67DRMXZSH5EZJ · pith_short_8: E3N67DRM

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/E3N67DRMXZSH5EZJTTVS257KRR \
  | 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: 26dbef8e2cbe647e93299ceb2d77ea8c79feed1db97f8d73580e0eb2dd5db8a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60053db8df410fe1efac20e0504b842965e37420782b492e33b319d87e8130b7",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-08-13T16:00:22Z",
    "title_canon_sha256": "745af4991fc0c6f6e47c22ca6bf121b79d38afc4e66ef9c177a350fce6faede4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.13402",
    "kind": "arxiv",
    "version": 1
  }
}