Pith Number

pith:3BSDIG64

pith:2015:3BSDIG64HSDCJVD46LSTXVQWOJ

not attested not anchored not stored refs pending

Proof of a conjecture of Graham and Lov\'asz concerning unimodality of coefficients of the distance characteristic polynomial of a tree

Aida Abiad, Franklin H. J. Kenter, Ghodratollah Aalipour, Jephian C.-H. Lin, Leslie Hogben, Michael Tait, Zhanar Berikkyzy

arxiv:1507.02341 v3 · 2015-07-09 · 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{3BSDIG64HSDCJVD46LSTXVQWOJ}

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	2026-05-18T00:46:04.685621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d864341bdc3c8624d47cf2e53bd6167249be9830f3c9c4a305f6f9e3268a1350

Aliases

arxiv: 1507.02341 · arxiv_version: 1507.02341v3 · doi: 10.48550/arxiv.1507.02341 · pith_short_12: 3BSDIG64HSDC · pith_short_16: 3BSDIG64HSDCJVD4 · pith_short_8: 3BSDIG64

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/3BSDIG64HSDCJVD46LSTXVQWOJ \
  | 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: d864341bdc3c8624d47cf2e53bd6167249be9830f3c9c4a305f6f9e3268a1350

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5b81536eb6dba192c320a0f7ff16a4d2f746f48916151f16825f5c73955d8b0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-07-09T01:04:49Z",
    "title_canon_sha256": "9d9411b9b451c351cafc50c7a8c691676d36c55d3db458722733464383bd4e89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.02341",
    "kind": "arxiv",
    "version": 3
  }
}