Pith Number

pith:ZXXSUTQX

pith:2012:ZXXSUTQXF3CY3HZFODWEYP232V

not attested not anchored not stored refs pending

Harmonic analysis on Cayley Trees II: the Bose Einstein condensation

Francesco Fidaleo

arxiv:1203.5522 v2 · 2012-03-25 · math-ph · cond-mat.supr-con · math.FA · math.MP · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZXXSUTQXF3CY3HZFODWEYP232V}

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	2026-05-18T03:56:47.365935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdef2a4e172ec58d9f2570ec4c3f5bd5708bc82458ec2a253155814764d01414

Aliases

arxiv: 1203.5522 · arxiv_version: 1203.5522v2 · doi: 10.48550/arxiv.1203.5522 · pith_short_12: ZXXSUTQXF3CY · pith_short_16: ZXXSUTQXF3CY3HZF · pith_short_8: ZXXSUTQX

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/ZXXSUTQXF3CY3HZFODWEYP232V \
  | 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: cdef2a4e172ec58d9f2570ec4c3f5bd5708bc82458ec2a253155814764d01414

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "85f23e25cdcc79642addee5c3fdeb0e01cd2c3a06b3bc19159de53a1f0197245",
    "cross_cats_sorted": [
      "cond-mat.supr-con",
      "math.FA",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-03-25T17:30:43Z",
    "title_canon_sha256": "e186782039cb11b3e2a6f1a84c6b6b050c442b535740724cc397d3f32b83a702"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5522",
    "kind": "arxiv",
    "version": 2
  }
}