Pith Number

pith:KTK4AFCV

pith:2026:KTK4AFCVJ5JB4JV4Q3P6PVRPSN

not attested not anchored not stored refs pending

The Goncharov Lie coalgebra of a field

Alexander Kupers, Daniil Rudenko, Ismael Sierra

arxiv:2606.23863 v1 · 2026-06-22 · math.KT · math.AT · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KTK4AFCVJ5JB4JV4Q3P6PVRPSN}

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	2026-06-24T00:14:28.852918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54d5c014554f521e26bc86dfe7d62f9378675a2b99cfe4e6bfbf2054662cba08

Aliases

arxiv: 2606.23863 · arxiv_version: 2606.23863v1 · doi: 10.48550/arxiv.2606.23863 · pith_short_12: KTK4AFCVJ5JB · pith_short_16: KTK4AFCVJ5JB4JV4 · pith_short_8: KTK4AFCV

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/KTK4AFCVJ5JB4JV4Q3P6PVRPSN \
  | 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: 54d5c014554f521e26bc86dfe7d62f9378675a2b99cfe4e6bfbf2054662cba08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10ec129ad37d4f423e78424d1e7ed46a78fdceefa9d418a2f86889f9e24182d7",
    "cross_cats_sorted": [
      "math.AT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2026-06-22T19:00:51Z",
    "title_canon_sha256": "4c00ec36fd194fe16206d08e9fec240ac2d12645d59fb84fb0447c68bc58d229"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23863",
    "kind": "arxiv",
    "version": 1
  }
}