Pith Number

pith:HLKMRYXQ

pith:2026:HLKMRYXQNL3CTZGUCEBBAL7FIB

not attested not anchored not stored refs pending

A Hilbert space embedding of persistence diagrams and barcodes

Peter Bubenik

arxiv:2608.08858 v1 · 2026-08-09 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HLKMRYXQNL3CTZGUCEBBAL7FIB}

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	2026-08-11T01:25:33.091495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ad4c8e2f06af629e4d41102102fe54059d1f70f5faaef52deb5cb5e47d2d434

Aliases

arxiv: 2608.08858 · arxiv_version: 2608.08858v1 · doi: 10.48550/arxiv.2608.08858 · pith_short_12: HLKMRYXQNL3C · pith_short_16: HLKMRYXQNL3CTZGU · pith_short_8: HLKMRYXQ

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/HLKMRYXQNL3CTZGUCEBBAL7FIB \
  | 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: 3ad4c8e2f06af629e4d41102102fe54059d1f70f5faaef52deb5cb5e47d2d434

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "941e60b44543072dfab3b58aefce7a281b39b3e31dfab70dd1314b23b7e5109b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-08-09T18:48:34Z",
    "title_canon_sha256": "2aec58b18634409e825dc57d5627b2a45f5de4b6e05bdaf6411977e697a3acba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.08858",
    "kind": "arxiv",
    "version": 1
  }
}