Pith Number

pith:ESUVV7H7

pith:2021:ESUVV7H77F5VJJT3IMF3OVF6SH

not attested not anchored not stored refs pending

Action of automorphisms of pure braid groups on homotopy groups of two-sphere

Ilya Alekseev, Mikhail Mikhailov, Vasily Ionin

arxiv:2112.05805 v2 · 2021-12-10 · math.GR · math.AT · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ESUVV7H77F5VJJT3IMF3OVF6SH}

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	2026-07-05T10:42:32.463878Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24a95afcfff97b54a67b430bb754be91f6289f7d77a16b43d440f579ccda7ac5

Aliases

arxiv: 2112.05805 · arxiv_version: 2112.05805v2 · doi: 10.48550/arxiv.2112.05805 · pith_short_12: ESUVV7H77F5V · pith_short_16: ESUVV7H77F5VJJT3 · pith_short_8: ESUVV7H7

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/ESUVV7H77F5VJJT3IMF3OVF6SH \
  | 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: 24a95afcfff97b54a67b430bb754be91f6289f7d77a16b43d440f579ccda7ac5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "632f4a9366936610139de506e672ea25253c2b9d9ad5a2ec546ed7c164bea35f",
    "cross_cats_sorted": [
      "math.AT",
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2021-12-10T19:50:19Z",
    "title_canon_sha256": "59e95e982f0982b87e1e156b73db6adbdb086cc2011cc7cbe730926741e11c6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.05805",
    "kind": "arxiv",
    "version": 2
  }
}