{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZBHIWL3L2BBI3Q5ZJNFQP5FEN6","short_pith_number":"pith:ZBHIWL3L","canonical_record":{"source":{"id":"1301.2358","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-10T23:42:47Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"eae1f013169dd620ded82243eb1e67ea75f77ccbc46dbbbdcfbadedc0d50f87b","abstract_canon_sha256":"adcc82ec0be1358ed48368429619ae4a6a5c94063d123fa9f9033c3821090b4d"},"schema_version":"1.0"},"canonical_sha256":"c84e8b2f6bd0428dc3b94b4b07f4a46fbb44d09ab7cd80c162b7b08b17077def","source":{"kind":"arxiv","id":"1301.2358","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2358","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2358v2","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2358","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"ZBHIWL3L2BBI","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZBHIWL3L2BBI3Q5Z","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZBHIWL3L","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZBHIWL3L2BBI3Q5ZJNFQP5FEN6","target":"record","payload":{"canonical_record":{"source":{"id":"1301.2358","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-10T23:42:47Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"eae1f013169dd620ded82243eb1e67ea75f77ccbc46dbbbdcfbadedc0d50f87b","abstract_canon_sha256":"adcc82ec0be1358ed48368429619ae4a6a5c94063d123fa9f9033c3821090b4d"},"schema_version":"1.0"},"canonical_sha256":"c84e8b2f6bd0428dc3b94b4b07f4a46fbb44d09ab7cd80c162b7b08b17077def","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:32.718324Z","signature_b64":"S4B9VH+s36eP5dtph41ZcLI9HzrjVQ3A+HIf+qDj08W5ypPGIOkiT2m5CuPgVCVDMc6QLEjMJv/JQiF3qSfrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c84e8b2f6bd0428dc3b94b4b07f4a46fbb44d09ab7cd80c162b7b08b17077def","last_reissued_at":"2026-05-18T02:58:32.717754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:32.717754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.2358","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":"2026-05-18T02:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZJO1SmQuLlFOodRk7qcdtrKvEFiEV8RSttguFdCwR3s7DVvn8FzzrpA3c9Jb+o8hjYTtQf/OPnBT1boLu6eTCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:04:15.492202Z"},"content_sha256":"96eead8362d148e47294a29fc36a97a2fa4d48e47df2c94a48d31797208ae2b7","schema_version":"1.0","event_id":"sha256:96eead8362d148e47294a29fc36a97a2fa4d48e47df2c94a48d31797208ae2b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZBHIWL3L2BBI3Q5ZJNFQP5FEN6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal velocity estimates and soft mode bounds for the massless spin-boson model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. Kupiainen, W. De Roeck","submitted_at":"2013-01-10T23:42:47Z","abstract_excerpt":"We consider generalised versions of the spin-boson model at small coupling. We assume the spin (or atom) to sit at the origin $0 \\in \\mathbb{R}^d$ and the propagation speed $v_p$ of free bosons to be constant, i.e.\\ independent of momentum. In particular, the bosons are massless. We prove detailed bounds on the mean number of bosons contained in the ball $\\{|x| \\leq v_p t \\}$. In particular, we prove that, as $t \\to \\infty$, this number tends to an asymptotic value that can be naturally identified as the mean number of bosons bound to the atom in the ground state. Physically, this means that b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2358","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":""},"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":"2026-05-18T02:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1uhhLMN5y4C6MbOLiNBvtXVoNFEAKqkp+Jumh2Jgn1xhuxRSxOkZAr9cUgZACgHwGBGz1mlNOv972oTAfkAQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T23:04:15.492570Z"},"content_sha256":"ca2815a0c605c69b186916da93d8a9086d063bc1261a8503dd40bd4f9c82f212","schema_version":"1.0","event_id":"sha256:ca2815a0c605c69b186916da93d8a9086d063bc1261a8503dd40bd4f9c82f212"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBHIWL3L2BBI3Q5ZJNFQP5FEN6/bundle.json","state_url":"https://pith.science/pith/ZBHIWL3L2BBI3Q5ZJNFQP5FEN6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBHIWL3L2BBI3Q5ZJNFQP5FEN6/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":"2026-06-20T23:04:15Z","links":{"resolver":"https://pith.science/pith/ZBHIWL3L2BBI3Q5ZJNFQP5FEN6","bundle":"https://pith.science/pith/ZBHIWL3L2BBI3Q5ZJNFQP5FEN6/bundle.json","state":"https://pith.science/pith/ZBHIWL3L2BBI3Q5ZJNFQP5FEN6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBHIWL3L2BBI3Q5ZJNFQP5FEN6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZBHIWL3L2BBI3Q5ZJNFQP5FEN6","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":"adcc82ec0be1358ed48368429619ae4a6a5c94063d123fa9f9033c3821090b4d","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-10T23:42:47Z","title_canon_sha256":"eae1f013169dd620ded82243eb1e67ea75f77ccbc46dbbbdcfbadedc0d50f87b"},"schema_version":"1.0","source":{"id":"1301.2358","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2358","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2358v2","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2358","created_at":"2026-05-18T02:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"ZBHIWL3L2BBI","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZBHIWL3L2BBI3Q5Z","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZBHIWL3L","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:ca2815a0c605c69b186916da93d8a9086d063bc1261a8503dd40bd4f9c82f212","target":"graph","created_at":"2026-05-18T02:58:32Z","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"},"paper":{"abstract_excerpt":"We consider generalised versions of the spin-boson model at small coupling. We assume the spin (or atom) to sit at the origin $0 \\in \\mathbb{R}^d$ and the propagation speed $v_p$ of free bosons to be constant, i.e.\\ independent of momentum. In particular, the bosons are massless. We prove detailed bounds on the mean number of bosons contained in the ball $\\{|x| \\leq v_p t \\}$. In particular, we prove that, as $t \\to \\infty$, this number tends to an asymptotic value that can be naturally identified as the mean number of bosons bound to the atom in the ground state. Physically, this means that b","authors_text":"A. Kupiainen, W. De Roeck","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-10T23:42:47Z","title":"Minimal velocity estimates and soft mode bounds for the massless spin-boson model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2358","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":"sha256:96eead8362d148e47294a29fc36a97a2fa4d48e47df2c94a48d31797208ae2b7","target":"record","created_at":"2026-05-18T02:58:32Z","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":"adcc82ec0be1358ed48368429619ae4a6a5c94063d123fa9f9033c3821090b4d","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-10T23:42:47Z","title_canon_sha256":"eae1f013169dd620ded82243eb1e67ea75f77ccbc46dbbbdcfbadedc0d50f87b"},"schema_version":"1.0","source":{"id":"1301.2358","kind":"arxiv","version":2}},"canonical_sha256":"c84e8b2f6bd0428dc3b94b4b07f4a46fbb44d09ab7cd80c162b7b08b17077def","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c84e8b2f6bd0428dc3b94b4b07f4a46fbb44d09ab7cd80c162b7b08b17077def","first_computed_at":"2026-05-18T02:58:32.717754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:32.717754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S4B9VH+s36eP5dtph41ZcLI9HzrjVQ3A+HIf+qDj08W5ypPGIOkiT2m5CuPgVCVDMc6QLEjMJv/JQiF3qSfrDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:32.718324Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2358","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96eead8362d148e47294a29fc36a97a2fa4d48e47df2c94a48d31797208ae2b7","sha256:ca2815a0c605c69b186916da93d8a9086d063bc1261a8503dd40bd4f9c82f212"],"state_sha256":"71c31abb52a82a92efb4dc0b29cc80a72751aa06d8cc2f4e9e34469b330f67a9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qDsl8TvSrI+0FhcgpAzl4N5ju4L/EU+OuayAUdYcoBfOOwpAAZJrJ+z8Vg2RpE0R7f8lNxSgBqkkHxj5VzHtCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T23:04:15.494478Z","bundle_sha256":"af0e1e5d9793db208c4c516d29cc0e1d50f4ec084bf83a7116b60e89def0dda5"}}