{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YFC42OQO475KY7HH2UQ6QKJHGT","short_pith_number":"pith:YFC42OQO","canonical_record":{"source":{"id":"1301.2961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-14T13:00:41Z","cross_cats_sorted":[],"title_canon_sha256":"a5c6931c25acdfbd244873ac2032b07fa5eeefb9a79735292b494ecf54028d5f","abstract_canon_sha256":"8c1b8654109f0a2ff49e9dc17b1b4651ae0747bfd0e20a12bb48cbea45f2a395"},"schema_version":"1.0"},"canonical_sha256":"c145cd3a0ee7faac7ce7d521e8292734e5da945a48fe23c18e98909cc5094493","source":{"kind":"arxiv","id":"1301.2961","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2961","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2961v1","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2961","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"YFC42OQO475K","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YFC42OQO475KY7HH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YFC42OQO","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YFC42OQO475KY7HH2UQ6QKJHGT","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2961","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-14T13:00:41Z","cross_cats_sorted":[],"title_canon_sha256":"a5c6931c25acdfbd244873ac2032b07fa5eeefb9a79735292b494ecf54028d5f","abstract_canon_sha256":"8c1b8654109f0a2ff49e9dc17b1b4651ae0747bfd0e20a12bb48cbea45f2a395"},"schema_version":"1.0"},"canonical_sha256":"c145cd3a0ee7faac7ce7d521e8292734e5da945a48fe23c18e98909cc5094493","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:27.722002Z","signature_b64":"w1K5jzTesnYkPe96qSDTANVOXFqYNGimHOLj10gRtrbrwrUh7z8vuqFhj18SDdXT9YPYHrixaZQ5XiPsl0m7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c145cd3a0ee7faac7ce7d521e8292734e5da945a48fe23c18e98909cc5094493","last_reissued_at":"2026-05-18T03:36:27.721477Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:27.721477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2961","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KU3gxrLMBl8jFGq7kgh6mP/G/6LHocpEqfEaFCPep0Vn6fwhqhx3O6SseOP9ReceqsPIsj9fjxfO///0xx92Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:18:02.542948Z"},"content_sha256":"d192f27d2ff9535595815ff7cc39eba5725bfb25d452cbb762c2e26ea9869035","schema_version":"1.0","event_id":"sha256:d192f27d2ff9535595815ff7cc39eba5725bfb25d452cbb762c2e26ea9869035"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YFC42OQO475KY7HH2UQ6QKJHGT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Sobolev trace Theorem for variable exponent spaces in the critical range","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Analia Silva, Julian Fernandez Bonder, Nicolas Saintier","submitted_at":"2013-01-14T13:00:41Z","abstract_excerpt":"In this paper we study the Sobolev Trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then we give local conditions on the exponents and on the domain (in the spirit of Adimurthy and Yadava) in order to satisfy such conditions, and therefore to ensure the existence of extremals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2961","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:36:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IvzNCgWDj0YOnzOg8PeLPmxXIpEwylLBPdXR9Walg5DycXBdDGwufblvGVfzX9aEu7jrqng3Cwkta7l+63dJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T20:18:02.543297Z"},"content_sha256":"283fccbbe57d7bcba0214b523776d5b7f868479e50dc45aa39510b7c878a2b10","schema_version":"1.0","event_id":"sha256:283fccbbe57d7bcba0214b523776d5b7f868479e50dc45aa39510b7c878a2b10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YFC42OQO475KY7HH2UQ6QKJHGT/bundle.json","state_url":"https://pith.science/pith/YFC42OQO475KY7HH2UQ6QKJHGT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YFC42OQO475KY7HH2UQ6QKJHGT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T20:18:02Z","links":{"resolver":"https://pith.science/pith/YFC42OQO475KY7HH2UQ6QKJHGT","bundle":"https://pith.science/pith/YFC42OQO475KY7HH2UQ6QKJHGT/bundle.json","state":"https://pith.science/pith/YFC42OQO475KY7HH2UQ6QKJHGT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YFC42OQO475KY7HH2UQ6QKJHGT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YFC42OQO475KY7HH2UQ6QKJHGT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8c1b8654109f0a2ff49e9dc17b1b4651ae0747bfd0e20a12bb48cbea45f2a395","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-14T13:00:41Z","title_canon_sha256":"a5c6931c25acdfbd244873ac2032b07fa5eeefb9a79735292b494ecf54028d5f"},"schema_version":"1.0","source":{"id":"1301.2961","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2961","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2961v1","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2961","created_at":"2026-05-18T03:36:27Z"},{"alias_kind":"pith_short_12","alias_value":"YFC42OQO475K","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YFC42OQO475KY7HH","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YFC42OQO","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:283fccbbe57d7bcba0214b523776d5b7f868479e50dc45aa39510b7c878a2b10","target":"graph","created_at":"2026-05-18T03:36:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper we study the Sobolev Trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then we give local conditions on the exponents and on the domain (in the spirit of Adimurthy and Yadava) in order to satisfy such conditions, and therefore to ensure the existence of extremals.","authors_text":"Analia Silva, Julian Fernandez Bonder, Nicolas Saintier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-14T13:00:41Z","title":"On the Sobolev trace Theorem for variable exponent spaces in the critical range"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2961","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d192f27d2ff9535595815ff7cc39eba5725bfb25d452cbb762c2e26ea9869035","target":"record","created_at":"2026-05-18T03:36:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8c1b8654109f0a2ff49e9dc17b1b4651ae0747bfd0e20a12bb48cbea45f2a395","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-14T13:00:41Z","title_canon_sha256":"a5c6931c25acdfbd244873ac2032b07fa5eeefb9a79735292b494ecf54028d5f"},"schema_version":"1.0","source":{"id":"1301.2961","kind":"arxiv","version":1}},"canonical_sha256":"c145cd3a0ee7faac7ce7d521e8292734e5da945a48fe23c18e98909cc5094493","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c145cd3a0ee7faac7ce7d521e8292734e5da945a48fe23c18e98909cc5094493","first_computed_at":"2026-05-18T03:36:27.721477Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:27.721477Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w1K5jzTesnYkPe96qSDTANVOXFqYNGimHOLj10gRtrbrwrUh7z8vuqFhj18SDdXT9YPYHrixaZQ5XiPsl0m7Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:27.722002Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2961","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d192f27d2ff9535595815ff7cc39eba5725bfb25d452cbb762c2e26ea9869035","sha256:283fccbbe57d7bcba0214b523776d5b7f868479e50dc45aa39510b7c878a2b10"],"state_sha256":"400a5de28a273942183eeb4aca32e2e1a197e0f97bf7ad587f003c55f157e2fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"85PbnXNFD4puDqMY4de+s4oc7E0xKXeDskKKE0Cs7nL8+qhyrb4Bu4gr8aj2A32QJBYG6pGFMkCOqheP44dpDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T20:18:02.545879Z","bundle_sha256":"518f7d7d3f8847cef3c5cf3e222dabee28f06aad3ba408fe11788661c328112c"}}