Pith Number

pith:QE4GV3AA

pith:2026:QE4GV3AADHX3F4W7TU7MUYYBKJ

not attested not anchored not stored refs pending

Sharp Lower Bounds on the Haraux Function Beyond Reflexivity

Weifeng Yang

arxiv:2608.13139 v1 · 2026-08-13 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QE4GV3AADHX3F4W7TU7MUYYBKJ}

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	2026-08-14T01:00:28.061820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81386aec0019efb2f2df9d3eca63015245c2ae6e718a6924b75da33e7a32db76

Aliases

arxiv: 2608.13139 · arxiv_version: 2608.13139v1 · doi: 10.48550/arxiv.2608.13139 · pith_short_12: QE4GV3AADHX3 · pith_short_16: QE4GV3AADHX3F4W7 · pith_short_8: QE4GV3AA

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/QE4GV3AADHX3F4W7TU7MUYYBKJ \
  | 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: 81386aec0019efb2f2df9d3eca63015245c2ae6e718a6924b75da33e7a32db76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2d821e2496a2e0a3d52b915710b74c695f42efa9e32f5a5dc88dc7167ef8df58",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2026-08-13T12:14:55Z",
    "title_canon_sha256": "eb022b6921470d9e2e9743e28c4cc583dddc917c7e68f46e995428b67e71540f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.13139",
    "kind": "arxiv",
    "version": 1
  }
}