Pith Number

pith:TBAJGMIX

pith:2026:TBAJGMIXNAVZ7QKERPGYGCD6EO

not attested not anchored not stored refs pending

Relations in the 24-th homotopy groups of spheres

Juno Mukai, Toshiyuki Miyauchi

arxiv:2606.12046 v1 · 2026-06-10 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TBAJGMIXNAVZ7QKERPGYGCD6EO}

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	2026-06-11T01:10:44.837075Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9840933117682b9fc1448bcd83087e23bfc76e663b1ea237d7ef00568d979e7d

Aliases

arxiv: 2606.12046 · arxiv_version: 2606.12046v1 · doi: 10.48550/arxiv.2606.12046 · pith_short_12: TBAJGMIXNAVZ · pith_short_16: TBAJGMIXNAVZ7QKE · pith_short_8: TBAJGMIX

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/TBAJGMIXNAVZ7QKERPGYGCD6EO \
  | 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: 9840933117682b9fc1448bcd83087e23bfc76e663b1ea237d7ef00568d979e7d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8e675568f52340cfe1756f51ebb8e491c3463c9b4dd56f2b438063c445b805aa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-06-10T13:12:23Z",
    "title_canon_sha256": "c63d523b5ac3875cfa854d7c86bc3de53b3999dd4899c17e0cfd4f187ab457e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12046",
    "kind": "arxiv",
    "version": 1
  }
}