Pith Number

pith:MI56FLYE

pith:2018:MI56FLYEX35NRLPVGZNSIA64GO

not attested not anchored not stored refs pending

The lower $p$-central series of a free profinite group and the shuffle algebra

Ido Efrat

arxiv:1808.05354 v1 · 2018-08-16 · math.NT · math.KT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MI56FLYEX35NRLPVGZNSIA64GO}

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	2026-05-18T00:07:57.404362Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

623be2af04befad8adf5365b2403dc33b5284db8754f7fd5e9821f2052b383aa

Aliases

arxiv: 1808.05354 · arxiv_version: 1808.05354v1 · doi: 10.48550/arxiv.1808.05354 · pith_short_12: MI56FLYEX35N · pith_short_16: MI56FLYEX35NRLPV · pith_short_8: MI56FLYE

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/MI56FLYEX35NRLPVGZNSIA64GO \
  | 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: 623be2af04befad8adf5365b2403dc33b5284db8754f7fd5e9821f2052b383aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "478c05d5e896054c2e84e04ec1f9c0e2deef5015076b4ab13fe27901876fd084",
    "cross_cats_sorted": [
      "math.KT",
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-08-16T06:13:37Z",
    "title_canon_sha256": "3e47a25ce909d15fa2ae482e3c84f1c12ece7cf286e8fab52bcd20a6b0edccf6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.05354",
    "kind": "arxiv",
    "version": 1
  }
}