Pith Number

pith:YFBHLCQ7

pith:2026:YFBHLCQ7ZM5OREY4BR2RQRIF5G

not attested not anchored not stored refs pending

A lower bound for relative symplectic cohomology barcode entropy

Jonghyeon Ahn

arxiv:2606.09164 v1 · 2026-06-08 · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YFBHLCQ7ZM5OREY4BR2RQRIF5G}

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	2026-06-09T02:08:04.005072Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c142758a1fcb3ae8931c0c75184505e9a778fa853c199fe250a6ad0e17e84985

Aliases

arxiv: 2606.09164 · arxiv_version: 2606.09164v1 · doi: 10.48550/arxiv.2606.09164 · pith_short_12: YFBHLCQ7ZM5O · pith_short_16: YFBHLCQ7ZM5OREY4 · pith_short_8: YFBHLCQ7

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/YFBHLCQ7ZM5OREY4BR2RQRIF5G \
  | 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: c142758a1fcb3ae8931c0c75184505e9a778fa853c199fe250a6ad0e17e84985

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42fd5f3f84a94be6ccd3b2626b9b9635a3448f886b68abf45603d8460072936f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2026-06-08T08:01:38Z",
    "title_canon_sha256": "d1c1f3b80becd81b081f193ad6e1e5be1b418ad78e5cc1a95c1301cc4b635b13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.09164",
    "kind": "arxiv",
    "version": 1
  }
}