{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:L5UGQZGRKZU4CYFVCD3MMESYIV","short_pith_number":"pith:L5UGQZGR","canonical_record":{"source":{"id":"2503.03076","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2025-03-05T00:31:42Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"4465979e0de8eee0d5eb34f8ec5b6a27bbd44414e22a08f190055b0843569848","abstract_canon_sha256":"99004eaaefff36e4c00481a84fad861138119aef0725a7d0abc6053285c72ef3"},"schema_version":"1.0"},"canonical_sha256":"5f686864d15669c160b510f6c61258457a0ecf12b282ce336a39dbc35c6e6062","source":{"kind":"arxiv","id":"2503.03076","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.03076","created_at":"2026-07-05T11:16:06Z"},{"alias_kind":"arxiv_version","alias_value":"2503.03076v2","created_at":"2026-07-05T11:16:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.03076","created_at":"2026-07-05T11:16:06Z"},{"alias_kind":"pith_short_12","alias_value":"L5UGQZGRKZU4","created_at":"2026-07-05T11:16:06Z"},{"alias_kind":"pith_short_16","alias_value":"L5UGQZGRKZU4CYFV","created_at":"2026-07-05T11:16:06Z"},{"alias_kind":"pith_short_8","alias_value":"L5UGQZGR","created_at":"2026-07-05T11:16:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:L5UGQZGRKZU4CYFVCD3MMESYIV","target":"record","payload":{"canonical_record":{"source":{"id":"2503.03076","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2025-03-05T00:31:42Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"4465979e0de8eee0d5eb34f8ec5b6a27bbd44414e22a08f190055b0843569848","abstract_canon_sha256":"99004eaaefff36e4c00481a84fad861138119aef0725a7d0abc6053285c72ef3"},"schema_version":"1.0"},"canonical_sha256":"5f686864d15669c160b510f6c61258457a0ecf12b282ce336a39dbc35c6e6062","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:16:06.746530Z","signature_b64":"nTk0OOYzCG45oOanugdIMnuVLOwLrMziwCMlXHKLyzrp1dOlciAqtT/cjy3acEU0lJgUqo4s45CxD1GVZfuGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f686864d15669c160b510f6c61258457a0ecf12b282ce336a39dbc35c6e6062","last_reissued_at":"2026-07-05T11:16:06.745953Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:16:06.745953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.03076","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:16:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zyNVqokC4LeHfuAmzNV9DxUExAOeRLEy98VObKSkvP5sIFZBZaSvSDvxAmwtLFoDIQOqk+Dd2mkIy47RnDCKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T18:24:19.343694Z"},"content_sha256":"3a249965a78773ff9fedd1d250bd8e9a27a142a7895e0f50ef5c135307e87410","schema_version":"1.0","event_id":"sha256:3a249965a78773ff9fedd1d250bd8e9a27a142a7895e0f50ef5c135307e87410"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:L5UGQZGRKZU4CYFVCD3MMESYIV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Abhijit Bhattacharyya, Debashis Gangopadhyay, Eduardo Guendelman, Goutam Manna, Samit Ganguly","submitted_at":"2025-03-05T00:31:42Z","abstract_excerpt":"We present a new avenue of the Raychaudhuri Equation (RE) by introducing a non-affine parametrization within the k-essence framework. This modification accounts for non-geodesic flow curves, leading to emergent repulsive effects in cosmic evolution. Using a DBI-type k-essence Lagrangian, we derive a modified RE and demonstrate its ability to address the Hubble tension while predicting a natural emergence of a dynamical dark energy equation of state. Our Bayesian analysis, constrained by cosmological data, supports the theoretical scaling relation of the k-essence field ($\\dot{\\phi}$) and the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.03076","kind":"arxiv","version":2},"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/2503.03076/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":"2026-07-05T11:16:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HwjZXNRc9Fb/0f9SWAbrG/gK/6+18ei7vj8gkWz6r8n7kU6PtlvClx2r+0m7T86CFxXZVJhZhCXI3n8kmOULBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T18:24:19.344205Z"},"content_sha256":"50ecdcabc0ebdf956a77c1e37419fed38587fda9d22e9af18994f841a92dbd46","schema_version":"1.0","event_id":"sha256:50ecdcabc0ebdf956a77c1e37419fed38587fda9d22e9af18994f841a92dbd46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5UGQZGRKZU4CYFVCD3MMESYIV/bundle.json","state_url":"https://pith.science/pith/L5UGQZGRKZU4CYFVCD3MMESYIV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5UGQZGRKZU4CYFVCD3MMESYIV/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":"2026-08-07T18:24:19Z","links":{"resolver":"https://pith.science/pith/L5UGQZGRKZU4CYFVCD3MMESYIV","bundle":"https://pith.science/pith/L5UGQZGRKZU4CYFVCD3MMESYIV/bundle.json","state":"https://pith.science/pith/L5UGQZGRKZU4CYFVCD3MMESYIV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5UGQZGRKZU4CYFVCD3MMESYIV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:L5UGQZGRKZU4CYFVCD3MMESYIV","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":"99004eaaefff36e4c00481a84fad861138119aef0725a7d0abc6053285c72ef3","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2025-03-05T00:31:42Z","title_canon_sha256":"4465979e0de8eee0d5eb34f8ec5b6a27bbd44414e22a08f190055b0843569848"},"schema_version":"1.0","source":{"id":"2503.03076","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.03076","created_at":"2026-07-05T11:16:06Z"},{"alias_kind":"arxiv_version","alias_value":"2503.03076v2","created_at":"2026-07-05T11:16:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.03076","created_at":"2026-07-05T11:16:06Z"},{"alias_kind":"pith_short_12","alias_value":"L5UGQZGRKZU4","created_at":"2026-07-05T11:16:06Z"},{"alias_kind":"pith_short_16","alias_value":"L5UGQZGRKZU4CYFV","created_at":"2026-07-05T11:16:06Z"},{"alias_kind":"pith_short_8","alias_value":"L5UGQZGR","created_at":"2026-07-05T11:16:06Z"}],"graph_snapshots":[{"event_id":"sha256:50ecdcabc0ebdf956a77c1e37419fed38587fda9d22e9af18994f841a92dbd46","target":"graph","created_at":"2026-07-05T11:16:06Z","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/2503.03076/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a new avenue of the Raychaudhuri Equation (RE) by introducing a non-affine parametrization within the k-essence framework. This modification accounts for non-geodesic flow curves, leading to emergent repulsive effects in cosmic evolution. Using a DBI-type k-essence Lagrangian, we derive a modified RE and demonstrate its ability to address the Hubble tension while predicting a natural emergence of a dynamical dark energy equation of state. Our Bayesian analysis, constrained by cosmological data, supports the theoretical scaling relation of the k-essence field ($\\dot{\\phi}$) and the c","authors_text":"Abhijit Bhattacharyya, Debashis Gangopadhyay, Eduardo Guendelman, Goutam Manna, Samit Ganguly","cross_cats":["hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2025-03-05T00:31:42Z","title":"Non-Affine Extensions of the Raychaudhuri Equation in the K-essence Framework"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.03076","kind":"arxiv","version":2},"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":"sha256:3a249965a78773ff9fedd1d250bd8e9a27a142a7895e0f50ef5c135307e87410","target":"record","created_at":"2026-07-05T11:16:06Z","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":"99004eaaefff36e4c00481a84fad861138119aef0725a7d0abc6053285c72ef3","cross_cats_sorted":["hep-th"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2025-03-05T00:31:42Z","title_canon_sha256":"4465979e0de8eee0d5eb34f8ec5b6a27bbd44414e22a08f190055b0843569848"},"schema_version":"1.0","source":{"id":"2503.03076","kind":"arxiv","version":2}},"canonical_sha256":"5f686864d15669c160b510f6c61258457a0ecf12b282ce336a39dbc35c6e6062","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f686864d15669c160b510f6c61258457a0ecf12b282ce336a39dbc35c6e6062","first_computed_at":"2026-07-05T11:16:06.745953Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:06.745953Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nTk0OOYzCG45oOanugdIMnuVLOwLrMziwCMlXHKLyzrp1dOlciAqtT/cjy3acEU0lJgUqo4s45CxD1GVZfuGCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:06.746530Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.03076","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a249965a78773ff9fedd1d250bd8e9a27a142a7895e0f50ef5c135307e87410","sha256:50ecdcabc0ebdf956a77c1e37419fed38587fda9d22e9af18994f841a92dbd46"],"state_sha256":"6cbc4d00f2bb6c6645351d0742ef4be4a05ee842e5fbebf8973ee002be418a4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0owGp7NkdAVMpi0ihBnyvkrOasr/Xs2UgYruh9CAMgZksCF50DOcSDb7g3W/afCMb4QBF3NNO/8XL4rAyMLPDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T18:24:19.349943Z","bundle_sha256":"6974ebb6491739ea1ca2a71f560aac55f4b8315fa79e85b8b42599f5919bca32"}}