Pith Number

pith:6PRD6TM6

pith:2026:6PRD6TM6BEJQZTFJYYJ2BZEOOE

not attested not anchored not stored refs pending

Sharp error estimates in stochastic homogenization of parabolic systems with time-dependent coefficients

Jun Geng, Qiang Xu

arxiv:2605.18201 v1 · 2026-05-18 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6PRD6TM6BEJQZTFJYYJ2BZEOOE}

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	2026-05-20T00:05:50.401351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3e23f4d9e09130ccca9c613a0e48e7101ff6ee30256b4f84bfb230aade95a92

Aliases

arxiv: 2605.18201 · arxiv_version: 2605.18201v1 · doi: 10.48550/arxiv.2605.18201 · pith_short_12: 6PRD6TM6BEJQ · pith_short_16: 6PRD6TM6BEJQZTFJ · pith_short_8: 6PRD6TM6

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/6PRD6TM6BEJQZTFJYYJ2BZEOOE \
  | 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: f3e23f4d9e09130ccca9c613a0e48e7101ff6ee30256b4f84bfb230aade95a92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44f1d43fea62b2459e517b7334e5304ea1396ec69f8a2c5ab726603265ba3c54",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-18T10:42:47Z",
    "title_canon_sha256": "fa5780da52b25b7a664d3b421308e0d15b45af83770fec8270b75cce8f451d9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.18201",
    "kind": "arxiv",
    "version": 1
  }
}