Pith Number

pith:3NSSD6YN

pith:2026:3NSSD6YNBRJNBMAUHRXC7R6MKU

not attested not anchored not stored refs pending

Learning the Graphical Nature of Symmetries

Adam Onus, Edward Hirst, Enrico Grimaldi, Harmeet Singh, Rashid Barket, Yacoub Hendi

arxiv:2607.12026 v1 · 2026-07-13 · stat.ML · cs.LG · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3NSSD6YNBRJNBMAUHRXC7R6MKU}

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	2026-07-15T00:21:28.637283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db6521fb0d0c52d0b0143c6e2fc7cc5518232dcbb39eeb3625e94cfb7f40fa3f

Aliases

arxiv: 2607.12026 · arxiv_version: 2607.12026v1 · doi: 10.48550/arxiv.2607.12026 · pith_short_12: 3NSSD6YNBRJN · pith_short_16: 3NSSD6YNBRJNBMAU · pith_short_8: 3NSSD6YN

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/3NSSD6YNBRJNBMAUHRXC7R6MKU \
  | 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: db6521fb0d0c52d0b0143c6e2fc7cc5518232dcbb39eeb3625e94cfb7f40fa3f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55e386caecd1bd7e2fffa1d9a7a0a4026979cc7f949b4843e640426b21016285",
    "cross_cats_sorted": [
      "cs.LG",
      "math.CO",
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-07-13T18:00:02Z",
    "title_canon_sha256": "28dda9368bf294654e06249df3ff0afcb38f15c1e18f7f0b9a80d6952b917552"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12026",
    "kind": "arxiv",
    "version": 1
  }
}