Pith Number

pith:ABFCTHBL

pith:2013:ABFCTHBLQGPYWJIFHU7VRCEZFR

not attested not anchored not stored refs pending

On the degeneration of tunnel numbers under connected sum

Ruifeng Qiu, Tao Li

arxiv:1310.5054 v2 · 2013-10-18 · 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{ABFCTHBLQGPYWJIFHU7VRCEZFR}

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	2026-05-18T03:09:32.776157Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

004a299c2b819f8b25053d3f5888992c7fcc77d1ccb6b58282683f698f6996cd

Aliases

arxiv: 1310.5054 · arxiv_version: 1310.5054v2 · doi: 10.48550/arxiv.1310.5054 · pith_short_12: ABFCTHBLQGPY · pith_short_16: ABFCTHBLQGPYWJIF · pith_short_8: ABFCTHBL

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/ABFCTHBLQGPYWJIFHU7VRCEZFR \
  | 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: 004a299c2b819f8b25053d3f5888992c7fcc77d1ccb6b58282683f698f6996cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a75d3fca39b74ede13d87627588a114eaded6da0a07547fd16591f11b00a4c4d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-10-18T15:18:01Z",
    "title_canon_sha256": "987ada890680f94cf430605f5d8f6be62d790b2455b2a9532e51235bbfda7387"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.5054",
    "kind": "arxiv",
    "version": 2
  }
}