Pith Number

pith:5XWRIUAC

pith:2015:5XWRIUAC6LHOXHQP5KHAV4NTVR

not attested not anchored not stored refs pending

The spectrum of the growth rate of the tunnel number is infinite

Kenneth L. Baker, Tsuyoshi Kobayashi, Yo'av Rieck

arxiv:1507.03317 v1 · 2015-07-13 · math.GT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5XWRIUAC6LHOXHQP5KHAV4NTVR}

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	2026-05-18T01:36:59.115549Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eded145002f2ceeb9e0fea8e0af1b3ac4c69a0018031d8c7b541e37f280d8a17

Aliases

arxiv: 1507.03317 · arxiv_version: 1507.03317v1 · doi: 10.48550/arxiv.1507.03317 · pith_short_12: 5XWRIUAC6LHO · pith_short_16: 5XWRIUAC6LHOXHQP · pith_short_8: 5XWRIUAC

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/5XWRIUAC6LHOXHQP5KHAV4NTVR \
  | 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: eded145002f2ceeb9e0fea8e0af1b3ac4c69a0018031d8c7b541e37f280d8a17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d525adde274e70d40029e5535d29c1f80a6fd062cb6095749008634ec9f1cca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-07-13T03:22:02Z",
    "title_canon_sha256": "793a5bfe0dc36c4fd1acd5e477fe87aae1c0214e386a90e47d91401c86722b7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.03317",
    "kind": "arxiv",
    "version": 1
  }
}