Pith Number

pith:HRVNPB2T

pith:2025:HRVNPB2TILA7EJJ3BDAUIVEPE2

not attested not anchored not stored refs pending

Homology in Combinatorial Refraction Billiards

Colin Defant, Derek Liu

arxiv:2502.06013 v2 · 2025-02-09 · 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{HRVNPB2TILA7EJJ3BDAUIVEPE2}

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	2026-07-05T10:54:43.048711Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c6ad7875342c1f2253b08c144548f268555770a8814706c84ef75cb8287fb6e

Aliases

arxiv: 2502.06013 · arxiv_version: 2502.06013v2 · doi: 10.48550/arxiv.2502.06013 · pith_short_12: HRVNPB2TILA7 · pith_short_16: HRVNPB2TILA7EJJ3 · pith_short_8: HRVNPB2T

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/HRVNPB2TILA7EJJ3BDAUIVEPE2 \
  | 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: 3c6ad7875342c1f2253b08c144548f268555770a8814706c84ef75cb8287fb6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e4cd215572cf1d6927e2ce3488e5bbd51df7c65bd78d91c09b99d6ecbf5c0f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-02-09T20:09:30Z",
    "title_canon_sha256": "6bd3160663b74cd9aef0d50b13f9646338ce81934721bbd2d861325510c8d22e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.06013",
    "kind": "arxiv",
    "version": 2
  }
}