{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:E7UHERZOB3445V2T7IVYM6AUYT","short_pith_number":"pith:E7UHERZO","canonical_record":{"source":{"id":"2606.17614","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-06-16T07:19:13Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"4c1d6ea8d4c50d2f38ed1de9d17e3c84fdc9f0d406749a4c5a2787106f49211d","abstract_canon_sha256":"27b2a057cd5dbde4bf6e60b22703a7fdedaa4384173b3a6a4b836c39adeea2af"},"schema_version":"1.0"},"canonical_sha256":"27e872472e0ef9ced753fa2b867814c4f3883b0bb769865c8473ed31973dddae","source":{"kind":"arxiv","id":"2606.17614","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17614","created_at":"2026-06-19T16:10:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17614v1","created_at":"2026-06-19T16:10:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17614","created_at":"2026-06-19T16:10:17Z"},{"alias_kind":"pith_short_12","alias_value":"E7UHERZOB344","created_at":"2026-06-19T16:10:17Z"},{"alias_kind":"pith_short_16","alias_value":"E7UHERZOB3445V2T","created_at":"2026-06-19T16:10:17Z"},{"alias_kind":"pith_short_8","alias_value":"E7UHERZO","created_at":"2026-06-19T16:10:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:E7UHERZOB3445V2T7IVYM6AUYT","target":"record","payload":{"canonical_record":{"source":{"id":"2606.17614","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-06-16T07:19:13Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"4c1d6ea8d4c50d2f38ed1de9d17e3c84fdc9f0d406749a4c5a2787106f49211d","abstract_canon_sha256":"27b2a057cd5dbde4bf6e60b22703a7fdedaa4384173b3a6a4b836c39adeea2af"},"schema_version":"1.0"},"canonical_sha256":"27e872472e0ef9ced753fa2b867814c4f3883b0bb769865c8473ed31973dddae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:17.282560Z","signature_b64":"h6RYGFe4uQVqhloscdG+fJl42A8A3kGO89HGOjKmYrmpoJKyw+6dtE1gR68hOF0fKgtVZ6bT9rEXuomO7HEICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27e872472e0ef9ced753fa2b867814c4f3883b0bb769865c8473ed31973dddae","last_reissued_at":"2026-06-19T16:10:17.282213Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:17.282213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.17614","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":"2026-06-19T16:10:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EF+KIBbCK83yH1WnzrMiijKs2YpDnuNxUMxT/98k01kH7rgnEfw6kYM1VtRhB4xNj2DftrMXnRuf4w7Awsu0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:06:04.110548Z"},"content_sha256":"e4dc8db01f4c01157fe7152544dd484b52d2ec6f6cb1a36485b533a41b88736a","schema_version":"1.0","event_id":"sha256:e4dc8db01f4c01157fe7152544dd484b52d2ec6f6cb1a36485b533a41b88736a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:E7UHERZOB3445V2T7IVYM6AUYT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Joint reconstruction of $H(z)$ and $f\\sigma_8(z)$ with physics informed neural networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph.CO","authors_text":"Konstantinos F. Dialektopoulos","submitted_at":"2026-06-16T07:19:13Z","abstract_excerpt":"We present a proof of concept for the joint reconstruction of the Hubble parameter $H(z)$ that assumes no dark energy equation of state and the growth rate of large scale structure $f\\sigma_8(z)$ using a physics informed neural network. Rather than fitting these two observables separately and checking their consistency post hoc, we couple them through the linear growth equation of general relativity directly during training, using the equation residual evaluated at collocation points via automatic differentiation as an additional loss term. The network employs a shared backbone feeding two ind"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17614","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/2606.17614/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":"2026-06-19T16:10:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fNRqQJ75Q2I6jsmCXNYUN+G+N/5B4z7OMpEFlSGcGiGMGyHH/9FRN15PsCGnhB21dlu+Kae7daN3vdKI1VNkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T15:06:04.110934Z"},"content_sha256":"801baf1ccd2e1312068631fd16fee559fc4be0ded99a0880f126617dbe9788f6","schema_version":"1.0","event_id":"sha256:801baf1ccd2e1312068631fd16fee559fc4be0ded99a0880f126617dbe9788f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E7UHERZOB3445V2T7IVYM6AUYT/bundle.json","state_url":"https://pith.science/pith/E7UHERZOB3445V2T7IVYM6AUYT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E7UHERZOB3445V2T7IVYM6AUYT/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":"2026-06-27T15:06:04Z","links":{"resolver":"https://pith.science/pith/E7UHERZOB3445V2T7IVYM6AUYT","bundle":"https://pith.science/pith/E7UHERZOB3445V2T7IVYM6AUYT/bundle.json","state":"https://pith.science/pith/E7UHERZOB3445V2T7IVYM6AUYT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E7UHERZOB3445V2T7IVYM6AUYT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:E7UHERZOB3445V2T7IVYM6AUYT","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":"27b2a057cd5dbde4bf6e60b22703a7fdedaa4384173b3a6a4b836c39adeea2af","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-06-16T07:19:13Z","title_canon_sha256":"4c1d6ea8d4c50d2f38ed1de9d17e3c84fdc9f0d406749a4c5a2787106f49211d"},"schema_version":"1.0","source":{"id":"2606.17614","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.17614","created_at":"2026-06-19T16:10:17Z"},{"alias_kind":"arxiv_version","alias_value":"2606.17614v1","created_at":"2026-06-19T16:10:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17614","created_at":"2026-06-19T16:10:17Z"},{"alias_kind":"pith_short_12","alias_value":"E7UHERZOB344","created_at":"2026-06-19T16:10:17Z"},{"alias_kind":"pith_short_16","alias_value":"E7UHERZOB3445V2T","created_at":"2026-06-19T16:10:17Z"},{"alias_kind":"pith_short_8","alias_value":"E7UHERZO","created_at":"2026-06-19T16:10:17Z"}],"graph_snapshots":[{"event_id":"sha256:801baf1ccd2e1312068631fd16fee559fc4be0ded99a0880f126617dbe9788f6","target":"graph","created_at":"2026-06-19T16:10:17Z","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/2606.17614/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a proof of concept for the joint reconstruction of the Hubble parameter $H(z)$ that assumes no dark energy equation of state and the growth rate of large scale structure $f\\sigma_8(z)$ using a physics informed neural network. Rather than fitting these two observables separately and checking their consistency post hoc, we couple them through the linear growth equation of general relativity directly during training, using the equation residual evaluated at collocation points via automatic differentiation as an additional loss term. The network employs a shared backbone feeding two ind","authors_text":"Konstantinos F. Dialektopoulos","cross_cats":["gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-06-16T07:19:13Z","title":"Joint reconstruction of $H(z)$ and $f\\sigma_8(z)$ with physics informed neural networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17614","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:e4dc8db01f4c01157fe7152544dd484b52d2ec6f6cb1a36485b533a41b88736a","target":"record","created_at":"2026-06-19T16:10:17Z","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":"27b2a057cd5dbde4bf6e60b22703a7fdedaa4384173b3a6a4b836c39adeea2af","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-06-16T07:19:13Z","title_canon_sha256":"4c1d6ea8d4c50d2f38ed1de9d17e3c84fdc9f0d406749a4c5a2787106f49211d"},"schema_version":"1.0","source":{"id":"2606.17614","kind":"arxiv","version":1}},"canonical_sha256":"27e872472e0ef9ced753fa2b867814c4f3883b0bb769865c8473ed31973dddae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27e872472e0ef9ced753fa2b867814c4f3883b0bb769865c8473ed31973dddae","first_computed_at":"2026-06-19T16:10:17.282213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:17.282213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h6RYGFe4uQVqhloscdG+fJl42A8A3kGO89HGOjKmYrmpoJKyw+6dtE1gR68hOF0fKgtVZ6bT9rEXuomO7HEICA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:17.282560Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.17614","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4dc8db01f4c01157fe7152544dd484b52d2ec6f6cb1a36485b533a41b88736a","sha256:801baf1ccd2e1312068631fd16fee559fc4be0ded99a0880f126617dbe9788f6"],"state_sha256":"9017c07beccca1cb30de43ebebcb28e0e3e8d47d77f5316259bfaca56be12bfd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"grTEfYG7uwDPPil79z24E3553Sjge0Ws3BAmAFi5xNhQ7aTvOBkGt8cLYdqUYMb5+MEmvNVWQ8IpJKE+66jzCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T15:06:04.112998Z","bundle_sha256":"9b415426c6ad22d519fefb8a938fa04a0153be19ad1f2898feea513b46ad81da"}}