Pith Number

pith:TLT7SH6Y

pith:2012:TLT7SH6YPFBKWSPIIOC6VPOD2J

not attested not anchored not stored refs pending

Sharp modulus of continuity for parabolic equations on manifolds and lower bounds for the first eigenvalue

Ben Andrews, Julie Clutterbuck

arxiv:1204.5079 v1 · 2012-04-23 · math.AP · math.DG · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TLT7SH6YPFBKWSPIIOC6VPOD2J}

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	2026-05-18T01:22:26.686885Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ae7f91fd87942ab49e84385eabdc3d26b88a0ce416e8e09d4f89f0885035d7d

Aliases

arxiv: 1204.5079 · arxiv_version: 1204.5079v1 · doi: 10.48550/arxiv.1204.5079 · pith_short_12: TLT7SH6YPFBK · pith_short_16: TLT7SH6YPFBKWSPI · pith_short_8: TLT7SH6Y

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/TLT7SH6YPFBKWSPIIOC6VPOD2J \
  | 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: 9ae7f91fd87942ab49e84385eabdc3d26b88a0ce416e8e09d4f89f0885035d7d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6df0d9a32e83c4780af6157f236535cecf38b1046064b4a610f53494b795e811",
    "cross_cats_sorted": [
      "math.DG",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-04-23T14:48:20Z",
    "title_canon_sha256": "43e18728784840dd008efaf587de06c2b22833875604f2b2d7caa33d8764d71e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.5079",
    "kind": "arxiv",
    "version": 1
  }
}