Pith Number

pith:2TYKDM37

pith:2026:2TYKDM37LRNC25QRVWXTQDPGZ7

not attested not anchored not stored refs pending

The Antipodes of $q$-Quasi-Symmetric Functions and Non-Commutative Quasi-Symmetric Functions

Shaul Zemel

arxiv:2607.07870 v1 · 2026-07-08 · 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{2TYKDM37LRNC25QRVWXTQDPGZ7}

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	2026-07-10T00:19:03.397581Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4f0a1b37f5c5a2d7611adaf380de6cfc048ab28361c7c4e9b8137eb960e340d

Aliases

arxiv: 2607.07870 · arxiv_version: 2607.07870v1 · doi: 10.48550/arxiv.2607.07870 · pith_short_12: 2TYKDM37LRNC · pith_short_16: 2TYKDM37LRNC25QR · pith_short_8: 2TYKDM37

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/2TYKDM37LRNC25QRVWXTQDPGZ7 \
  | 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: d4f0a1b37f5c5a2d7611adaf380de6cfc048ab28361c7c4e9b8137eb960e340d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af18dd2e45069d538f44eb0096ab77cba63b9f907e9169224c4a2ded0d5bc9eb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-08T19:15:04Z",
    "title_canon_sha256": "8762cf96b5e2a7f56bb5e62fe6aca9b811aa7c3c44f58f7d1613761695b34eef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.07870",
    "kind": "arxiv",
    "version": 1
  }
}