Pith Number

pith:H6UCBRBT

pith:2020:H6UCBRBT4ZMCQYFWNJQDT5NWMH

not attested not anchored not stored refs pending

Intersection between pencils of tubes, discretized sum-product, and radial projections

Bochen Liu, Chun-Yen Shen

arxiv:2001.02551 v1 · 2020-01-08 · math.CA · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{H6UCBRBT4ZMCQYFWNJQDT5NWMH}

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	2026-07-05T00:32:18.972935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3fa820c433e6582860b66a6039f5b661f06c32d6c6bf5c31db4edbac52a78f2f

Aliases

arxiv: 2001.02551 · arxiv_version: 2001.02551v1 · doi: 10.48550/arxiv.2001.02551 · pith_short_12: H6UCBRBT4ZMC · pith_short_16: H6UCBRBT4ZMCQYFW · pith_short_8: H6UCBRBT

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/H6UCBRBT4ZMCQYFWNJQDT5NWMH \
  | 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: 3fa820c433e6582860b66a6039f5b661f06c32d6c6bf5c31db4edbac52a78f2f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3348d9c461861e3a3cea7a89bbd2d9d66f28ae1f148079a61450202a674b0ae7",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2020-01-08T14:46:34Z",
    "title_canon_sha256": "92923b2234702511b0afe0e407cd892e9cef3d9d28b7d52dd07d20f89f2e7728"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.02551",
    "kind": "arxiv",
    "version": 1
  }
}