Pith Number

pith:33KFK355

pith:2026:33KFK355OBUALRTHW7GX64GNU7

not attested not anchored not stored refs pending

Khovanov homology: pro-tangles, derived colimits and spectral sequences

Jian Liu, Kefeng Liu, Li Shen

arxiv:2606.13471 v1 · 2026-06-11 · 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{33KFK355OBUALRTHW7GX64GNU7}

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	2026-06-12T01:10:04.265859Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ded4556fbd706805c667b7cd7f70cda7cc6c086b719e749e79efba854da826ff

Aliases

arxiv: 2606.13471 · arxiv_version: 2606.13471v1 · doi: 10.48550/arxiv.2606.13471 · pith_short_12: 33KFK355OBUA · pith_short_16: 33KFK355OBUALRTH · pith_short_8: 33KFK355

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/33KFK355OBUALRTHW7GX64GNU7 \
  | 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: ded4556fbd706805c667b7cd7f70cda7cc6c086b719e749e79efba854da826ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "925b939008e4ad856287df6f7cc85d645f21cf6c6b978e3e8f653549678c17df",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-06-11T15:23:57Z",
    "title_canon_sha256": "250e5d17ee12a0576ba7dc6fec54ac077a35c2237dd80092b2caab58a3f55a1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.13471",
    "kind": "arxiv",
    "version": 1
  }
}