Pith Number

pith:UID7K2AJ

pith:2010:UID7K2AJPFPJ22EC37A7GWZLW4

not attested not anchored not stored refs pending

Automorphisms of infinite Johnson graph

Mark Pankov

arxiv:1011.2407 v3 · 2010-11-10 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UID7K2AJPFPJ22EC37A7GWZLW4}

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	2026-05-18T04:32:35.174079Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a207f56809795e9d6882dfc1f35b2bb70a81871d13ca363e05500b00d5f28c68

Aliases

arxiv: 1011.2407 · arxiv_version: 1011.2407v3 · doi: 10.48550/arxiv.1011.2407 · pith_short_12: UID7K2AJPFPJ · pith_short_16: UID7K2AJPFPJ22EC · pith_short_8: UID7K2AJ

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/UID7K2AJPFPJ22EC37A7GWZLW4 \
  | 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: a207f56809795e9d6882dfc1f35b2bb70a81871d13ca363e05500b00d5f28c68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "645c9b4ca8eead67301b56802535d3d105c6697863d912466c5cc0441e2f5bbe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-11-10T15:34:21Z",
    "title_canon_sha256": "6db9d07cdd500811f809493f94fc7508e4acfea89ebf87df31bba654acbf82ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2407",
    "kind": "arxiv",
    "version": 3
  }
}