Pith Number

pith:I2ILKMX5

pith:2026:I2ILKMX5IZ5RQBBRAXJREFR56D

not attested not anchored not stored refs pending

On the toric lifting properties for simplicial $3$-spheres

Hyeontae Jang, Suyoung Choi, Yuanxin Guan, Zhi L\"u

arxiv:2607.18706 v1 · 2026-07-21 · math.AT · 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{I2ILKMX5IZ5RQBBRAXJREFR56D}

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	2026-07-22T01:23:07.579098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4690b532fd467b18043105d312163df0e02e4d17524a903f492853faa6221fe4

Aliases

arxiv: 2607.18706 · arxiv_version: 2607.18706v1 · doi: 10.48550/arxiv.2607.18706 · pith_short_12: I2ILKMX5IZ5R · pith_short_16: I2ILKMX5IZ5RQBBR · pith_short_8: I2ILKMX5

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/I2ILKMX5IZ5RQBBRAXJREFR56D \
  | 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: 4690b532fd467b18043105d312163df0e02e4d17524a903f492853faa6221fe4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdb28cd911bd28bce8aacc898ba4f39e652b677ff89dd7a86fac1ee099eae838",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-07-21T05:03:22Z",
    "title_canon_sha256": "be556965a73ff521e0e739fef2bb7c0b87ce87d9bdb2a887e184e61f0da0fbb5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.18706",
    "kind": "arxiv",
    "version": 1
  }
}