Pith Number

pith:B6TSX2R7

pith:2012:B6TSX2R7E7P6WLXZNDK437S4SW

not attested not anchored not stored refs pending

The Magnus expansion, trees and Knuth's rotation correspondence

Dominique Manchon, Kurusch Ebrahimi-Fard

arxiv:1203.2878 v1 · 2012-03-13 · math.CO · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B6TSX2R7E7P6WLXZNDK437S4SW}

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	2026-05-18T01:55:34.314053Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0fa72bea3f27dfeb2ef968d5cdfe5c95a49e8955d3587233b9196615939659ba

Aliases

arxiv: 1203.2878 · arxiv_version: 1203.2878v1 · doi: 10.48550/arxiv.1203.2878 · pith_short_12: B6TSX2R7E7P6 · pith_short_16: B6TSX2R7E7P6WLXZ · pith_short_8: B6TSX2R7

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/B6TSX2R7E7P6WLXZNDK437S4SW \
  | 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: 0fa72bea3f27dfeb2ef968d5cdfe5c95a49e8955d3587233b9196615939659ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f27b02dcbf2dff054c51a71ce47649c8e9b4970a22125df86e1827ae19fc5690",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-03-13T17:55:27Z",
    "title_canon_sha256": "8918d3f41ecf55d169321ae2cd01c054d14a4964e83f5c10fa9a0cd3ade8c86f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.2878",
    "kind": "arxiv",
    "version": 1
  }
}