{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4K3SQODRS3LMNIRBSD3ECQFQGS","short_pith_number":"pith:4K3SQODR","canonical_record":{"source":{"id":"2506.13891","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-16T18:14:44Z","cross_cats_sorted":[],"title_canon_sha256":"9780960076baeb48c028d25bc3ed202efcc49b1f232389bf9d13df3c336f2888","abstract_canon_sha256":"e79af3160719cc935e135b07d84117cacf8a63f708b7d1fad3b2acf548d9b6f5"},"schema_version":"1.0"},"canonical_sha256":"e2b728387196d6c6a22190f64140b034961edfca54aa3c73cb8c4df43a5774d3","source":{"kind":"arxiv","id":"2506.13891","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.13891","created_at":"2026-06-09T02:07:04Z"},{"alias_kind":"arxiv_version","alias_value":"2506.13891v3","created_at":"2026-06-09T02:07:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.13891","created_at":"2026-06-09T02:07:04Z"},{"alias_kind":"pith_short_12","alias_value":"4K3SQODRS3LM","created_at":"2026-06-09T02:07:04Z"},{"alias_kind":"pith_short_16","alias_value":"4K3SQODRS3LMNIRB","created_at":"2026-06-09T02:07:04Z"},{"alias_kind":"pith_short_8","alias_value":"4K3SQODR","created_at":"2026-06-09T02:07:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4K3SQODRS3LMNIRBSD3ECQFQGS","target":"record","payload":{"canonical_record":{"source":{"id":"2506.13891","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-16T18:14:44Z","cross_cats_sorted":[],"title_canon_sha256":"9780960076baeb48c028d25bc3ed202efcc49b1f232389bf9d13df3c336f2888","abstract_canon_sha256":"e79af3160719cc935e135b07d84117cacf8a63f708b7d1fad3b2acf548d9b6f5"},"schema_version":"1.0"},"canonical_sha256":"e2b728387196d6c6a22190f64140b034961edfca54aa3c73cb8c4df43a5774d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:07:04.526900Z","signature_b64":"tMtppoItddZFO+Nr1lrYYJJ5Ru6E+zeKpsWYM+IT+d9gmBfzIGVfUfMHW4+8AdAQ97A0kzWLp/ffW0ab8SltBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2b728387196d6c6a22190f64140b034961edfca54aa3c73cb8c4df43a5774d3","last_reissued_at":"2026-06-09T02:07:04.525812Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:07:04.525812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.13891","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T02:07:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8ycYwainTbrZqZ7K5UtIV85g5B8np2AqBfH6NQkPN6ew6YyM59NTNmERW/6wY+vp6GcMkAuYOXMIflD1tcGJAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:00:58.875432Z"},"content_sha256":"ecbac3173fc908c918f1d754597245a66097239981899ad78d25e65b2b1dd3ae","schema_version":"1.0","event_id":"sha256:ecbac3173fc908c918f1d754597245a66097239981899ad78d25e65b2b1dd3ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4K3SQODRS3LMNIRBSD3ECQFQGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Poincar\\'e Constants in three-dimensional Annuli","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bernd Rummler, Gudrun Th\\\"ater, Michael Ruzicka","submitted_at":"2025-06-16T18:14:44Z","abstract_excerpt":"We study 3d-annuli. In our non-dimensional setting each annulus ${\\Omega}_{\\cal A}$ is defined via two concentrical balls with radii ${\\cal A}/2$ and ${\\cal A}/2 +1$. For these geometries we provide the exact value for the Poincar\\'e constants for scalar functions and calculate precise Poincar\\'e constants for solenoidal vector fields (in both cases with vanishing Dirichlet traces on the boundary). For this we use the first eigenvalues of the scalar Laplacian and the Stokes operator, respectively. Additionally, corresponding problems in domains ${\\Omega}_{\\sigma}^{*}$, the 3d-annuli are invest"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13891","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.13891/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-09T02:07:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CRnOYIinbsVqxXr5ryuqerbjN+vx2BmV51koT+SO6Fvdwur/dKY2X4fpy0f3pYWSofpWBhX9rsc707bBhf0iAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:00:58.875833Z"},"content_sha256":"680b845263f4324612812821045a1f1c1d81310484e0553f2e7dfa17c89193dc","schema_version":"1.0","event_id":"sha256:680b845263f4324612812821045a1f1c1d81310484e0553f2e7dfa17c89193dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4K3SQODRS3LMNIRBSD3ECQFQGS/bundle.json","state_url":"https://pith.science/pith/4K3SQODRS3LMNIRBSD3ECQFQGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4K3SQODRS3LMNIRBSD3ECQFQGS/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":"2026-06-23T00:00:58Z","links":{"resolver":"https://pith.science/pith/4K3SQODRS3LMNIRBSD3ECQFQGS","bundle":"https://pith.science/pith/4K3SQODRS3LMNIRBSD3ECQFQGS/bundle.json","state":"https://pith.science/pith/4K3SQODRS3LMNIRBSD3ECQFQGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4K3SQODRS3LMNIRBSD3ECQFQGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4K3SQODRS3LMNIRBSD3ECQFQGS","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":"e79af3160719cc935e135b07d84117cacf8a63f708b7d1fad3b2acf548d9b6f5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-16T18:14:44Z","title_canon_sha256":"9780960076baeb48c028d25bc3ed202efcc49b1f232389bf9d13df3c336f2888"},"schema_version":"1.0","source":{"id":"2506.13891","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.13891","created_at":"2026-06-09T02:07:04Z"},{"alias_kind":"arxiv_version","alias_value":"2506.13891v3","created_at":"2026-06-09T02:07:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.13891","created_at":"2026-06-09T02:07:04Z"},{"alias_kind":"pith_short_12","alias_value":"4K3SQODRS3LM","created_at":"2026-06-09T02:07:04Z"},{"alias_kind":"pith_short_16","alias_value":"4K3SQODRS3LMNIRB","created_at":"2026-06-09T02:07:04Z"},{"alias_kind":"pith_short_8","alias_value":"4K3SQODR","created_at":"2026-06-09T02:07:04Z"}],"graph_snapshots":[{"event_id":"sha256:680b845263f4324612812821045a1f1c1d81310484e0553f2e7dfa17c89193dc","target":"graph","created_at":"2026-06-09T02:07:04Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.13891/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study 3d-annuli. In our non-dimensional setting each annulus ${\\Omega}_{\\cal A}$ is defined via two concentrical balls with radii ${\\cal A}/2$ and ${\\cal A}/2 +1$. For these geometries we provide the exact value for the Poincar\\'e constants for scalar functions and calculate precise Poincar\\'e constants for solenoidal vector fields (in both cases with vanishing Dirichlet traces on the boundary). For this we use the first eigenvalues of the scalar Laplacian and the Stokes operator, respectively. Additionally, corresponding problems in domains ${\\Omega}_{\\sigma}^{*}$, the 3d-annuli are invest","authors_text":"Bernd Rummler, Gudrun Th\\\"ater, Michael Ruzicka","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-16T18:14:44Z","title":"Exact Poincar\\'e Constants in three-dimensional Annuli"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13891","kind":"arxiv","version":3},"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:ecbac3173fc908c918f1d754597245a66097239981899ad78d25e65b2b1dd3ae","target":"record","created_at":"2026-06-09T02:07:04Z","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":"e79af3160719cc935e135b07d84117cacf8a63f708b7d1fad3b2acf548d9b6f5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-16T18:14:44Z","title_canon_sha256":"9780960076baeb48c028d25bc3ed202efcc49b1f232389bf9d13df3c336f2888"},"schema_version":"1.0","source":{"id":"2506.13891","kind":"arxiv","version":3}},"canonical_sha256":"e2b728387196d6c6a22190f64140b034961edfca54aa3c73cb8c4df43a5774d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2b728387196d6c6a22190f64140b034961edfca54aa3c73cb8c4df43a5774d3","first_computed_at":"2026-06-09T02:07:04.525812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:04.525812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tMtppoItddZFO+Nr1lrYYJJ5Ru6E+zeKpsWYM+IT+d9gmBfzIGVfUfMHW4+8AdAQ97A0kzWLp/ffW0ab8SltBw==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:04.526900Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.13891","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecbac3173fc908c918f1d754597245a66097239981899ad78d25e65b2b1dd3ae","sha256:680b845263f4324612812821045a1f1c1d81310484e0553f2e7dfa17c89193dc"],"state_sha256":"0ab684e8e9ea8e47e792c9638a5f9b0f1f3af7dc62f8ccf25730d6d545111327"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZOtvWonTXrQBhaXF+wiT7/2vx1FsAyjm3OEB6QF8v8Ik7XOST/ujo9Qov+8+ckJh/bsIgMmnYDaCPEzn0rL1BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:00:58.877904Z","bundle_sha256":"79f4af187e31db78748d22bdc99729bac0b5add143f0db1c6095863f577e51dd"}}