Pith Number

pith:2E2BBJDM

pith:2006:2E2BBJDMVREZGRYZ4TCN2TXQLD

not attested not anchored not stored refs pending

Congruences Compatible with the Shuffle Product

G\'erard Henry Edmond Duchamp (LIPN), Jean-Gabriel Luque (IGM-LabInfo)

arxiv:math/0607419 v1 · 2006-07-18 · math.CO · math.GM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2E2BBJDMVREZGRYZ4TCN2TXQLD}

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	2026-05-18T01:08:50.051642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d13410a46cac49934719e4c4dd4ef058e771f8759ed140ea6a407d4ef7d8239f

Aliases

arxiv: math/0607419 · arxiv_version: math/0607419v1 · doi: 10.48550/arxiv.math/0607419 · pith_short_12: 2E2BBJDMVREZ · pith_short_16: 2E2BBJDMVREZGRYZ · pith_short_8: 2E2BBJDM

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/2E2BBJDMVREZGRYZ4TCN2TXQLD \
  | 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: d13410a46cac49934719e4c4dd4ef058e771f8759ed140ea6a407d4ef7d8239f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cde86cfcdc869cb33580c5985cb598e2fa642912d4992d0c3266abae89da9636",
    "cross_cats_sorted": [
      "math.GM"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2006-07-18T12:20:09Z",
    "title_canon_sha256": "5288286fa6f9dc65ab844efa361a5596d0b03af2df2ef3300727ccc6efddbe4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0607419",
    "kind": "arxiv",
    "version": 1
  }
}