Pith Number

pith:KT3Q2EVU

pith:2015:KT3Q2EVULYLV7F2UAI3JXRIYDW

not attested not anchored not stored refs pending

Counterexamples to a conjecture of Balasubramanian and Parthasarathy

Shunyi Liu

arxiv:1502.01886 v1 · 2015-02-06 · 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{KT3Q2EVULYLV7F2UAI3JXRIYDW}

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	2026-05-18T00:43:45.560343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54f70d12b45e175f975402369bc5181d9ca6d52ef17f39fb0f37b32579c958a5

Aliases

arxiv: 1502.01886 · arxiv_version: 1502.01886v1 · doi: 10.48550/arxiv.1502.01886 · pith_short_12: KT3Q2EVULYLV · pith_short_16: KT3Q2EVULYLV7F2U · pith_short_8: KT3Q2EVU

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/KT3Q2EVULYLV7F2UAI3JXRIYDW \
  | 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: 54f70d12b45e175f975402369bc5181d9ca6d52ef17f39fb0f37b32579c958a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b2eb817b34182811e8c023528ab1d4d475d986a1ae0e89050d732d36b94c4cde",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-02-06T13:56:40Z",
    "title_canon_sha256": "52c94c937c820adfe267545f62546a5db2f7d5647b7b1f115727656478e14f40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.01886",
    "kind": "arxiv",
    "version": 1
  }
}