Pith Number

pith:CLRSSN3V

pith:2015:CLRSSN3VVT7KTE7BZL4LIYXAIF

not attested not anchored not stored refs pending

(Pure) transcendence bases in $\phi$-deformed shuffle bialgebras

Christophe Tollu (LIPN), G\'erard H.E. Duchamp (LIPN), Quoc Hoan Ng\^o (LIPN), Van Chi\^en Bui (LIPN), Vincel Hoang Ngoc Minh (LIPN)

arxiv:1507.01089 v2 · 2015-07-04 · cs.SC · math-ph · math.CO · math.GR · 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{CLRSSN3VVT7KTE7BZL4LIYXAIF}

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	2026-05-18T00:12:50.994603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12e3293775acfea993e1caf8b462e0414de1af4bcac73e6bc32996352f663535

Aliases

arxiv: 1507.01089 · arxiv_version: 1507.01089v2 · doi: 10.48550/arxiv.1507.01089 · pith_short_12: CLRSSN3VVT7K · pith_short_16: CLRSSN3VVT7KTE7B · pith_short_8: CLRSSN3V

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/CLRSSN3VVT7KTE7BZL4LIYXAIF \
  | 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: 12e3293775acfea993e1caf8b462e0414de1af4bcac73e6bc32996352f663535

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ae53065d52c1d859c7a915352f6bfa551b7c2db4392860848403f593a3c85ae",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.GR",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.SC",
    "submitted_at": "2015-07-04T09:25:07Z",
    "title_canon_sha256": "4186792308a08f8212fde4616dea410ddff74f7b890d5a6f4398b2c67390c394"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.01089",
    "kind": "arxiv",
    "version": 2
  }
}