{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:2HLZB2B6MIXNFJCNX7GDJSRIPO","short_pith_number":"pith:2HLZB2B6","canonical_record":{"source":{"id":"2506.18914","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-06-08T01:58:04Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"6a9d8a6f98cf542f1bcf7ce7cd5fca891465e80a50b85f3fa20a5dffa4936fbf","abstract_canon_sha256":"c05e42129f00b583315430f9a827460f3815c839f89387a352b75171fb3efd82"},"schema_version":"1.0"},"canonical_sha256":"d1d790e83e622ed2a44dbfcc34ca287bbea85086172471a5abe867e9403be061","source":{"kind":"arxiv","id":"2506.18914","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.18914","created_at":"2026-07-05T11:26:06Z"},{"alias_kind":"arxiv_version","alias_value":"2506.18914v1","created_at":"2026-07-05T11:26:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18914","created_at":"2026-07-05T11:26:06Z"},{"alias_kind":"pith_short_12","alias_value":"2HLZB2B6MIXN","created_at":"2026-07-05T11:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"2HLZB2B6MIXNFJCN","created_at":"2026-07-05T11:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"2HLZB2B6","created_at":"2026-07-05T11:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:2HLZB2B6MIXNFJCNX7GDJSRIPO","target":"record","payload":{"canonical_record":{"source":{"id":"2506.18914","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-06-08T01:58:04Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"6a9d8a6f98cf542f1bcf7ce7cd5fca891465e80a50b85f3fa20a5dffa4936fbf","abstract_canon_sha256":"c05e42129f00b583315430f9a827460f3815c839f89387a352b75171fb3efd82"},"schema_version":"1.0"},"canonical_sha256":"d1d790e83e622ed2a44dbfcc34ca287bbea85086172471a5abe867e9403be061","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:26:06.504307Z","signature_b64":"InZ3XoZO28/lHG4u5WmkwB5Dy/lAX6f0xaXGj0jsLs1CZFH+mJEideSDciv5Vj5yogHZkIBVGV9KR8aq5Vc2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1d790e83e622ed2a44dbfcc34ca287bbea85086172471a5abe867e9403be061","last_reissued_at":"2026-07-05T11:26:06.503928Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:26:06.503928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.18914","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":"2026-07-05T11:26:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u+TnyrZKPPWZeNZZfguC5nflip2KUtZIunTu+iDXK244tWN2AJxpFwoxL/A6PpVFqLVGg8FFI1J4vwA762PZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:18:17.106894Z"},"content_sha256":"9ce81107e7e6ec97ded5ac63edfdcab96b6ca1d92d62b8b121a661c4d5dee5c3","schema_version":"1.0","event_id":"sha256:9ce81107e7e6ec97ded5ac63edfdcab96b6ca1d92d62b8b121a661c4d5dee5c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:2HLZB2B6MIXNFJCNX7GDJSRIPO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Essential Self-Adjointness of the Geometric Deformation Operator on a Compact Interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.SP","authors_text":"Anton Alexa","submitted_at":"2025-06-08T01:58:04Z","abstract_excerpt":"We define a second-order differential operator $\\hat{C}$ on the Hilbert space $L^2([-v_c, v_c])$, constructed from a smooth deformation function $C(v)$. The operator is considered on the Sobolev domain $H^2([-v_c, v_c]) \\cap H^1_0([-v_c, v_c])$ with Dirichlet boundary conditions. We prove that $\\hat{C}$ is essentially self-adjoint by verifying its symmetry and computing von Neumann deficiency indices, which vanish. All steps are carried out explicitly. This result ensures the mathematical consistency of the operator and enables future spectral analysis on compact intervals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18914","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.18914/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":"2026-07-05T11:26:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8H5pJJn4FVYg58R2UPbWM9cPy1g5e6myzuu0YsIvT94+Onld3ftDHvfpt7neftIZJTAqDoRm02hrpKh6L6ZOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:18:17.107508Z"},"content_sha256":"903f96a7b26b57576b94df890a35864f5c2a4451162e7297274cf081d8c6da15","schema_version":"1.0","event_id":"sha256:903f96a7b26b57576b94df890a35864f5c2a4451162e7297274cf081d8c6da15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2HLZB2B6MIXNFJCNX7GDJSRIPO/bundle.json","state_url":"https://pith.science/pith/2HLZB2B6MIXNFJCNX7GDJSRIPO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2HLZB2B6MIXNFJCNX7GDJSRIPO/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":"2026-08-08T19:18:17Z","links":{"resolver":"https://pith.science/pith/2HLZB2B6MIXNFJCNX7GDJSRIPO","bundle":"https://pith.science/pith/2HLZB2B6MIXNFJCNX7GDJSRIPO/bundle.json","state":"https://pith.science/pith/2HLZB2B6MIXNFJCNX7GDJSRIPO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2HLZB2B6MIXNFJCNX7GDJSRIPO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2HLZB2B6MIXNFJCNX7GDJSRIPO","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":"c05e42129f00b583315430f9a827460f3815c839f89387a352b75171fb3efd82","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-06-08T01:58:04Z","title_canon_sha256":"6a9d8a6f98cf542f1bcf7ce7cd5fca891465e80a50b85f3fa20a5dffa4936fbf"},"schema_version":"1.0","source":{"id":"2506.18914","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.18914","created_at":"2026-07-05T11:26:06Z"},{"alias_kind":"arxiv_version","alias_value":"2506.18914v1","created_at":"2026-07-05T11:26:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.18914","created_at":"2026-07-05T11:26:06Z"},{"alias_kind":"pith_short_12","alias_value":"2HLZB2B6MIXN","created_at":"2026-07-05T11:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"2HLZB2B6MIXNFJCN","created_at":"2026-07-05T11:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"2HLZB2B6","created_at":"2026-07-05T11:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:903f96a7b26b57576b94df890a35864f5c2a4451162e7297274cf081d8c6da15","target":"graph","created_at":"2026-07-05T11:26:06Z","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/2506.18914/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define a second-order differential operator $\\hat{C}$ on the Hilbert space $L^2([-v_c, v_c])$, constructed from a smooth deformation function $C(v)$. The operator is considered on the Sobolev domain $H^2([-v_c, v_c]) \\cap H^1_0([-v_c, v_c])$ with Dirichlet boundary conditions. We prove that $\\hat{C}$ is essentially self-adjoint by verifying its symmetry and computing von Neumann deficiency indices, which vanish. All steps are carried out explicitly. This result ensures the mathematical consistency of the operator and enables future spectral analysis on compact intervals.","authors_text":"Anton Alexa","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-06-08T01:58:04Z","title":"Essential Self-Adjointness of the Geometric Deformation Operator on a Compact Interval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.18914","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":"sha256:9ce81107e7e6ec97ded5ac63edfdcab96b6ca1d92d62b8b121a661c4d5dee5c3","target":"record","created_at":"2026-07-05T11:26:06Z","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":"c05e42129f00b583315430f9a827460f3815c839f89387a352b75171fb3efd82","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2025-06-08T01:58:04Z","title_canon_sha256":"6a9d8a6f98cf542f1bcf7ce7cd5fca891465e80a50b85f3fa20a5dffa4936fbf"},"schema_version":"1.0","source":{"id":"2506.18914","kind":"arxiv","version":1}},"canonical_sha256":"d1d790e83e622ed2a44dbfcc34ca287bbea85086172471a5abe867e9403be061","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1d790e83e622ed2a44dbfcc34ca287bbea85086172471a5abe867e9403be061","first_computed_at":"2026-07-05T11:26:06.503928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:26:06.503928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"InZ3XoZO28/lHG4u5WmkwB5Dy/lAX6f0xaXGj0jsLs1CZFH+mJEideSDciv5Vj5yogHZkIBVGV9KR8aq5Vc2Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:26:06.504307Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.18914","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ce81107e7e6ec97ded5ac63edfdcab96b6ca1d92d62b8b121a661c4d5dee5c3","sha256:903f96a7b26b57576b94df890a35864f5c2a4451162e7297274cf081d8c6da15"],"state_sha256":"17b7d25195c23891a0c0f4dc5e9fe4f61b0882ae2f52f7f49535bbdd5f3f894a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oPIvOhEL415/uhjG1vppAcSMKZW4Jh5AKrlae+4qFizcjI/ww7ElZcSQU5ho2i1vnkL8CzfPhv7fYs1kiP4TCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T19:18:17.111890Z","bundle_sha256":"ffa0990ba0a09cf2a3cacbd6c5ee8e8198d46359c2740840d017c0a96d1d9ebc"}}