Pith Number

pith:SKPQN4MJ

pith:2015:SKPQN4MJZKKITJ5VBGAWXZ5MDB

not attested not anchored not stored refs pending

A combinatorial Hopf algebra for the boson normal ordering problem

Ali Chouria, Imad Eddine Bousbaa, Jean-Gabriel Luque

arxiv:1512.05937 v2 · 2015-12-18 · math.CO · 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{SKPQN4MJZKKITJ5VBGAWXZ5MDB}

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	2026-05-18T00:24:04.696405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

929f06f189ca9489a7b509816be7ac18417b18ce3776bf216a93d5fc057781e9

Aliases

arxiv: 1512.05937 · arxiv_version: 1512.05937v2 · doi: 10.48550/arxiv.1512.05937 · pith_short_12: SKPQN4MJZKKI · pith_short_16: SKPQN4MJZKKITJ5V · pith_short_8: SKPQN4MJ

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/SKPQN4MJZKKITJ5VBGAWXZ5MDB \
  | 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: 929f06f189ca9489a7b509816be7ac18417b18ce3776bf216a93d5fc057781e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00c1b7849dcc6b699154c87fdbb3898f9d77a2874e8ed056ef4647bdda883bd7",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-18T13:14:55Z",
    "title_canon_sha256": "a98bff1502bc766ef3bf0881314f86b7c3a418cb6edecbb501450e5331afb574"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05937",
    "kind": "arxiv",
    "version": 2
  }
}