Pith Number

pith:VXEDFS2M

pith:2016:VXEDFS2M5SGIKGVRNWUNMUA7PA

not attested not anchored not stored refs pending

Proof of a Conjecture of Kleinberg-Sawin-Speyer

Luke Pebody

arxiv:1608.05740 v3 · 2016-08-19 · 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{VXEDFS2M5SGIKGVRNWUNMUA7PA}

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	2026-05-18T00:11:28.333687Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

adc832cb4cec8c851ab16da8d6501f78132224f3a01d6ef6d7f4fcfe9ee3af57

Aliases

arxiv: 1608.05740 · arxiv_version: 1608.05740v3 · doi: 10.48550/arxiv.1608.05740 · pith_short_12: VXEDFS2M5SGI · pith_short_16: VXEDFS2M5SGIKGVR · pith_short_8: VXEDFS2M

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/VXEDFS2M5SGIKGVRNWUNMUA7PA \
  | 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: adc832cb4cec8c851ab16da8d6501f78132224f3a01d6ef6d7f4fcfe9ee3af57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fa385413bf6735bd5bda7cd3bb6480dcffcd0800e3b12826af378872fe7f2c9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-08-19T21:19:40Z",
    "title_canon_sha256": "6f524545fcd021c74b0075ad4cf57ab1d7aa77f24f3439d203cfab51e1484365"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.05740",
    "kind": "arxiv",
    "version": 3
  }
}