Pith Number

pith:GC4A3GMF

pith:2015:GC4A3GMFX3E7XHYNXAIMPNSQSM

not attested not anchored not stored refs pending

Directed paths: from Ramsey to Ruzsa and Szemer\'edi

Po-Shen Loh

arxiv:1505.07312 v2 · 2015-05-27 · 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{GC4A3GMFX3E7XHYNXAIMPNSQSM}

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	2026-05-18T01:29:20.936190Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30b80d9985bec9fb9f0db810c7b650932834cf26bc37b5a47b135ee79109e8e9

Aliases

arxiv: 1505.07312 · arxiv_version: 1505.07312v2 · doi: 10.48550/arxiv.1505.07312 · pith_short_12: GC4A3GMFX3E7 · pith_short_16: GC4A3GMFX3E7XHYN · pith_short_8: GC4A3GMF

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/GC4A3GMFX3E7XHYNXAIMPNSQSM \
  | 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: 30b80d9985bec9fb9f0db810c7b650932834cf26bc37b5a47b135ee79109e8e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "53df5d2d8bc8a041e46c17501fe13ee5ac27469b1db92f12c2dd59ebbd3efad4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-05-27T13:39:19Z",
    "title_canon_sha256": "db18f9b982b3933dbefc6a697ce5df31dfb7f789d87d08d01ae0c5689e9610fa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.07312",
    "kind": "arxiv",
    "version": 2
  }
}