Pith Number

pith:ZBARDDSP

pith:2012:ZBARDDSPI4UXXNEYUJU34NHYTG

not attested not anchored not stored refs pending

Hodge-de Rham Theory on Fractal Graphs and Fractals

Hui Yu, Robert Strichartz, Skye Aaron, Zach Conn

arxiv:1206.1310 v1 · 2012-06-06 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZBARDDSPI4UXXNEYUJU34NHYTG}

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	2026-05-18T03:54:06.453620Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c841118e4f47297bb498a269be34f8999348072cf07c31226a00b98b5e043c41

Aliases

arxiv: 1206.1310 · arxiv_version: 1206.1310v1 · doi: 10.48550/arxiv.1206.1310 · pith_short_12: ZBARDDSPI4UX · pith_short_16: ZBARDDSPI4UXXNEY · pith_short_8: ZBARDDSP

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/ZBARDDSPI4UXXNEYUJU34NHYTG \
  | 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: c841118e4f47297bb498a269be34f8999348072cf07c31226a00b98b5e043c41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7e8cafc0f9fff534da8a79934e0a1aa363ab970f4bd985d8894182cda409632c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-06-06T19:36:11Z",
    "title_canon_sha256": "5658c0367a016b5c1d35b7aeb39a14dc8985702635627f6d3e010b6ed9fb29f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.1310",
    "kind": "arxiv",
    "version": 1
  }
}