{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:T7FPKUZHHJETRHQEWRZUSTHSHQ","short_pith_number":"pith:T7FPKUZH","canonical_record":{"source":{"id":"2604.08142","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-09T12:01:28Z","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-ph"],"title_canon_sha256":"aead9b54fbed323657bfff7403883b5fe5bae61a662a543e78800d2de22f883d","abstract_canon_sha256":"be2cd9ac47c6e83dec48718080ac202f25a91f15f6cd3362400c736354bc0941"},"schema_version":"1.0"},"canonical_sha256":"9fcaf553273a49389e04b473494cf23c2e3c8bc0f24beae94943ef66be6e83d6","source":{"kind":"arxiv","id":"2604.08142","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.08142","created_at":"2026-06-24T01:15:02Z"},{"alias_kind":"arxiv_version","alias_value":"2604.08142v2","created_at":"2026-06-24T01:15:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.08142","created_at":"2026-06-24T01:15:02Z"},{"alias_kind":"pith_short_12","alias_value":"T7FPKUZHHJET","created_at":"2026-06-24T01:15:02Z"},{"alias_kind":"pith_short_16","alias_value":"T7FPKUZHHJETRHQE","created_at":"2026-06-24T01:15:02Z"},{"alias_kind":"pith_short_8","alias_value":"T7FPKUZH","created_at":"2026-06-24T01:15:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:T7FPKUZHHJETRHQEWRZUSTHSHQ","target":"record","payload":{"canonical_record":{"source":{"id":"2604.08142","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-09T12:01:28Z","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-ph"],"title_canon_sha256":"aead9b54fbed323657bfff7403883b5fe5bae61a662a543e78800d2de22f883d","abstract_canon_sha256":"be2cd9ac47c6e83dec48718080ac202f25a91f15f6cd3362400c736354bc0941"},"schema_version":"1.0"},"canonical_sha256":"9fcaf553273a49389e04b473494cf23c2e3c8bc0f24beae94943ef66be6e83d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-24T01:15:02.714240Z","signature_b64":"h+O0KSK7x932tpxedqSV+z9wBwgV9BCvNgyW/0BEKird7Uj0XRhjbS2AVrJA0JSfcf+ElM+DrWqzgr09OSU5Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fcaf553273a49389e04b473494cf23c2e3c8bc0f24beae94943ef66be6e83d6","last_reissued_at":"2026-06-24T01:15:02.713822Z","signature_status":"signed_v1","first_computed_at":"2026-06-24T01:15:02.713822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2604.08142","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":"2026-06-24T01:15:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ltUi9LoJjWS6NRybXVMr1JeN/Sc5hvzMWl5O4FNRMzqpIfwv7HlmSghzdxEd4qoQpGWExZpOo/Zw5KlsvKSeBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:12:28.890246Z"},"content_sha256":"fa4d295ef25256fc9e7115880ed4b3954f153434454bac4f85e2cb1bdbad9416","schema_version":"1.0","event_id":"sha256:fa4d295ef25256fc9e7115880ed4b3954f153434454bac4f85e2cb1bdbad9416"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:T7FPKUZHHJETRHQEWRZUSTHSHQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Caustic formation in DBI models: Wave propagation on planar domain walls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The DBI model for planar domain walls prevents caustic formation from smooth waves in the hyperbolic regime.","cross_cats":["astro-ph.CO","gr-qc","hep-ph"],"primary_cat":"hep-th","authors_text":"B. Gafarov, E. Babichev, M. Valencia-Villegas, S. Ramazanov","submitted_at":"2026-04-09T12:01:28Z","abstract_excerpt":"We investigate propagation of generic waves on thin planar domain walls effectively described by the scalar Dirac-Born-Infeld model (DBI). We pay a particular attention to the possibility of caustic formation - the process, which may lead to intensive particle emission by domain walls. It is demonstrated that no singularities arise in DBI in 2D flat spacetime in the hyperbolic case, if one starts from smooth initial conditions. Technically, this happens because the same family characteristics of the relevant partial differential equation remain parallel at all the times, albeit not being strai"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we prove that DBI remains shock free in the hyperbolic case in all these physically relevant situations. This strongly suggests that caustics can form on planar domain walls only due to the loss of hyperbolicity, and they have a cusp profile.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The effective scalar DBI description remains valid and the system stays inside the hyperbolic regime; the analysis does not address what happens once hyperbolicity is lost or when higher-order corrections become important.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"DBI domain walls stay shock-free in the hyperbolic regime across 2D flat space and extended physical setups, with caustics forming only upon loss of hyperbolicity and exhibiting cusp profiles.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The DBI model for planar domain walls prevents caustic formation from smooth waves in the hyperbolic regime.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f9072efc86590c1aeaff941ae4349dc3f264cb46308a20eccafcea695a024874"},"source":{"id":"2604.08142","kind":"arxiv","version":2},"verdict":{"id":"9f82be73-3ec2-4031-8cb4-d319b1da78d8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T18:05:00.880383Z","strongest_claim":"we prove that DBI remains shock free in the hyperbolic case in all these physically relevant situations. This strongly suggests that caustics can form on planar domain walls only due to the loss of hyperbolicity, and they have a cusp profile.","one_line_summary":"DBI domain walls stay shock-free in the hyperbolic regime across 2D flat space and extended physical setups, with caustics forming only upon loss of hyperbolicity and exhibiting cusp profiles.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The effective scalar DBI description remains valid and the system stays inside the hyperbolic regime; the analysis does not address what happens once hyperbolicity is lost or when higher-order corrections become important.","pith_extraction_headline":"The DBI model for planar domain walls prevents caustic formation from smooth waves in the hyperbolic regime."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.08142/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":"9f82be73-3ec2-4031-8cb4-d319b1da78d8"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-24T01:15:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fJK51TY3To2uMCOuEJi4eUD2zsM68aO7SmN/QjgVEU5LNTs5NlhAOLxAdWCqku+POzXaotUYp2xdS/mAIzcwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T15:12:28.890910Z"},"content_sha256":"4bb395d9eb4b583ec6b6d268c42424566792a4859ef944ed895b5bb3be819c5a","schema_version":"1.0","event_id":"sha256:4bb395d9eb4b583ec6b6d268c42424566792a4859ef944ed895b5bb3be819c5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T7FPKUZHHJETRHQEWRZUSTHSHQ/bundle.json","state_url":"https://pith.science/pith/T7FPKUZHHJETRHQEWRZUSTHSHQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T7FPKUZHHJETRHQEWRZUSTHSHQ/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":"2026-08-04T15:12:28Z","links":{"resolver":"https://pith.science/pith/T7FPKUZHHJETRHQEWRZUSTHSHQ","bundle":"https://pith.science/pith/T7FPKUZHHJETRHQEWRZUSTHSHQ/bundle.json","state":"https://pith.science/pith/T7FPKUZHHJETRHQEWRZUSTHSHQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T7FPKUZHHJETRHQEWRZUSTHSHQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:T7FPKUZHHJETRHQEWRZUSTHSHQ","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":"be2cd9ac47c6e83dec48718080ac202f25a91f15f6cd3362400c736354bc0941","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-09T12:01:28Z","title_canon_sha256":"aead9b54fbed323657bfff7403883b5fe5bae61a662a543e78800d2de22f883d"},"schema_version":"1.0","source":{"id":"2604.08142","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.08142","created_at":"2026-06-24T01:15:02Z"},{"alias_kind":"arxiv_version","alias_value":"2604.08142v2","created_at":"2026-06-24T01:15:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.08142","created_at":"2026-06-24T01:15:02Z"},{"alias_kind":"pith_short_12","alias_value":"T7FPKUZHHJET","created_at":"2026-06-24T01:15:02Z"},{"alias_kind":"pith_short_16","alias_value":"T7FPKUZHHJETRHQE","created_at":"2026-06-24T01:15:02Z"},{"alias_kind":"pith_short_8","alias_value":"T7FPKUZH","created_at":"2026-06-24T01:15:02Z"}],"graph_snapshots":[{"event_id":"sha256:4bb395d9eb4b583ec6b6d268c42424566792a4859ef944ed895b5bb3be819c5a","target":"graph","created_at":"2026-06-24T01:15:02Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"we prove that DBI remains shock free in the hyperbolic case in all these physically relevant situations. This strongly suggests that caustics can form on planar domain walls only due to the loss of hyperbolicity, and they have a cusp profile."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The effective scalar DBI description remains valid and the system stays inside the hyperbolic regime; the analysis does not address what happens once hyperbolicity is lost or when higher-order corrections become important."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"DBI domain walls stay shock-free in the hyperbolic regime across 2D flat space and extended physical setups, with caustics forming only upon loss of hyperbolicity and exhibiting cusp profiles."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The DBI model for planar domain walls prevents caustic formation from smooth waves in the hyperbolic regime."}],"snapshot_sha256":"f9072efc86590c1aeaff941ae4349dc3f264cb46308a20eccafcea695a024874"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.08142/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate propagation of generic waves on thin planar domain walls effectively described by the scalar Dirac-Born-Infeld model (DBI). We pay a particular attention to the possibility of caustic formation - the process, which may lead to intensive particle emission by domain walls. It is demonstrated that no singularities arise in DBI in 2D flat spacetime in the hyperbolic case, if one starts from smooth initial conditions. Technically, this happens because the same family characteristics of the relevant partial differential equation remain parallel at all the times, albeit not being strai","authors_text":"B. Gafarov, E. Babichev, M. Valencia-Villegas, S. Ramazanov","cross_cats":["astro-ph.CO","gr-qc","hep-ph"],"headline":"The DBI model for planar domain walls prevents caustic formation from smooth waves in the hyperbolic regime.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-09T12:01:28Z","title":"Caustic formation in DBI models: Wave propagation on planar domain walls"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.08142","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T18:05:00.880383Z","id":"9f82be73-3ec2-4031-8cb4-d319b1da78d8","model_set":{"reader":"grok-4.3"},"one_line_summary":"DBI domain walls stay shock-free in the hyperbolic regime across 2D flat space and extended physical setups, with caustics forming only upon loss of hyperbolicity and exhibiting cusp profiles.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The DBI model for planar domain walls prevents caustic formation from smooth waves in the hyperbolic regime.","strongest_claim":"we prove that DBI remains shock free in the hyperbolic case in all these physically relevant situations. This strongly suggests that caustics can form on planar domain walls only due to the loss of hyperbolicity, and they have a cusp profile.","weakest_assumption":"The effective scalar DBI description remains valid and the system stays inside the hyperbolic regime; the analysis does not address what happens once hyperbolicity is lost or when higher-order corrections become important."}},"verdict_id":"9f82be73-3ec2-4031-8cb4-d319b1da78d8"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fa4d295ef25256fc9e7115880ed4b3954f153434454bac4f85e2cb1bdbad9416","target":"record","created_at":"2026-06-24T01:15:02Z","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":"be2cd9ac47c6e83dec48718080ac202f25a91f15f6cd3362400c736354bc0941","cross_cats_sorted":["astro-ph.CO","gr-qc","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-04-09T12:01:28Z","title_canon_sha256":"aead9b54fbed323657bfff7403883b5fe5bae61a662a543e78800d2de22f883d"},"schema_version":"1.0","source":{"id":"2604.08142","kind":"arxiv","version":2}},"canonical_sha256":"9fcaf553273a49389e04b473494cf23c2e3c8bc0f24beae94943ef66be6e83d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fcaf553273a49389e04b473494cf23c2e3c8bc0f24beae94943ef66be6e83d6","first_computed_at":"2026-06-24T01:15:02.713822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:02.713822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h+O0KSK7x932tpxedqSV+z9wBwgV9BCvNgyW/0BEKird7Uj0XRhjbS2AVrJA0JSfcf+ElM+DrWqzgr09OSU5Bw==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:02.714240Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.08142","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa4d295ef25256fc9e7115880ed4b3954f153434454bac4f85e2cb1bdbad9416","sha256:4bb395d9eb4b583ec6b6d268c42424566792a4859ef944ed895b5bb3be819c5a"],"state_sha256":"9fe5ea074011a6fa272669377997b7c176dea6d9b12a7531d0936b943feceecb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GRgwnH9jDzRwox1nTILqYT6OXPol7W6zHNPXCePeXQiS0DJxYW8Jflo9Yw5Ps4CnLtngtzfGs2HJjPhaVIpuAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T15:12:28.894721Z","bundle_sha256":"aa129839c8b61f19ed0c2166b4f599db0a02121cb888bf2c2d86a0f5ed77723b"}}