Pith Number

pith:6KN5KHG2

pith:2020:6KN5KHG2FZNGKKMTGRMDJ2LSR2

not attested not anchored not stored refs pending

Spectral properties of the non-backtracking matrix of a graph

Cory Glover, Mark Kempton

arxiv:2011.09385 v1 · 2020-11-18 · 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{6KN5KHG2FZNGKKMTGRMDJ2LSR2}

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.

Cited by

1 paper in Pith

Subgroups of a free group with every growth rate

Receipt and verification

First computed	2026-07-05T01:52:43.534237Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f29bd51cda2e5a652993345834e9728eb2d42978a165e0c6d3931123fff31332

Aliases

arxiv: 2011.09385 · arxiv_version: 2011.09385v1 · doi: 10.48550/arxiv.2011.09385 · pith_short_12: 6KN5KHG2FZNG · pith_short_16: 6KN5KHG2FZNGKKMT · pith_short_8: 6KN5KHG2

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/6KN5KHG2FZNGKKMTGRMDJ2LSR2 \
  | 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: f29bd51cda2e5a652993345834e9728eb2d42978a165e0c6d3931123fff31332

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7b4a62615916750f9c9c135cf2f4523fb2876345c6c69056e62d114828900b5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-11-18T16:34:51Z",
    "title_canon_sha256": "f8ade57848e386b771939e4c2e7496b365a0ba583ca7b635a615bd33a47feccc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2011.09385",
    "kind": "arxiv",
    "version": 1
  }
}