Pith Number

pith:22WXJPPR

pith:2018:22WXJPPRRC63JGGTEUWTKJIWRW

not attested not anchored not stored refs pending

Refined $q$-Trinomial Coefficients and Two Infinite Hierarchies of $q$-Series Identities

Alexander Berkovich, Ali K. Uncu

arxiv:1810.12048 v2 · 2018-10-29 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{22WXJPPRRC63JGGTEUWTKJIWRW}

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	2026-05-17T23:50:06.836625Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6ad74bdf188bdb498d3252d3525168d867b04820ece1579f69de542def6b417

Aliases

arxiv: 1810.12048 · arxiv_version: 1810.12048v2 · doi: 10.48550/arxiv.1810.12048 · pith_short_12: 22WXJPPRRC63 · pith_short_16: 22WXJPPRRC63JGGT · pith_short_8: 22WXJPPR

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/22WXJPPRRC63JGGTEUWTKJIWRW \
  | 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: d6ad74bdf188bdb498d3252d3525168d867b04820ece1579f69de542def6b417

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f378820779787186e40dcd2aacb027157faad4b5837edaa06a31163ed2c75dea",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-10-29T10:43:06Z",
    "title_canon_sha256": "380b8c240e5fe052ff7eaa8136b52e45fb0fb56c3fce23a34ba3d2677f070a08"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.12048",
    "kind": "arxiv",
    "version": 2
  }
}